Use trigonometric identities to verify each expression is equal. csc2(x) - 2csc(x)cot(x) + cot2(x) = tan2(x/2)

Answers

Answer 1

By definition of csc and cot,

csc²(x) - 2 csc(x) cot(x) + cot²(x) = …

… = 1/sin²(x) - 2 cos(x) / sin²(x) + cos²(x) / sin²(x)

Combining fractions,

… = (1 - 2 cos(x) + cos²(x)) / sin²(x)

Factorize the numerator and use the Pythagorean identity,

cos²(x) + sin²(x) = 1,

to rewrite the denominator.

… = (1 - cos(x))² / (1 - cos²(x))

Cancel a factor of 1 - cos(x).

… = (1 - cos(x)) / (1 + cos(x))

Using the half-angle identities,

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

it follows that

1 - cos(x) = 2 sin²(x/2)

1 + cos(x) = 2 cos²(x/2)

and so

… = (2 sin²(x/2)) / (2 cos²(x/2))

… = sin²(x/2) / cos²(x/2)

Finally, by definition of tangent,

… = tan²(x/2)


Related Questions

If you have a choice to earn simple interest on $10,000 for three years at 8% or annually compounded interest at 7. 5% for three years which one will pay more and by how much?.

Answers

Answer:

annually compounded interest at 7. 5% for three years will pay more by $22.97

Explanation:

Simple interest

A = P (1+ rt)

A = final amount

P = initial principal balance

r = interest rate

t = number of time periods elapsed

A = 10000(1+0.08x3) = $12,400

Annual compound interest

A = P (1+ r/n)^nt

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

A = 10000(1+0.075/1)^(1x3) = $12,422.97

$12,422.97 - $12,400 = $22.97

akao wrote an opinion piece about why he thinks sandwiches are the perfect food. Read the first body paragraph.

Sandwiches make healthy food taste good. You can choose a soft whole grain bread as a base. Then you can add a lean meat or some other protein, like hummus. Finally, some lettuce or other greens will give it a nice, healthy crunch.

Which sentence states the reason for Takao’s opinion?
A. "Sandwiches can be tasty and healthy too."
B. "You can choose a soft whole grain bread as a base."
C. "Then you can add a lean meat or some other protein, like hummus.
D. "Finally, some lettuce or other greens will give it a nice, healthy crunch."

Answers

Answer:

A

Not confident about this answer, so sorry if it is wrong

Explanation:

I think it is a because

It is the topic sentence

The sentence is also the only sentence to entirely be an opinion

The rest of the paragraph is talking about what you can put on it to make it taste good and be healthy

How does frankenstein feel about his creation brainly.

Answers

I would say, he was pretty dang happy! Let me tell you, juggling kids, work and school! It’s crazy but this app helps me so much with my math. I really do appreciate how it explains the answer. Thank you!!

Which of the following statements about the administration of cpr is true?.

Answers

Explanation:

hope this will helps you

How can you protect yourself from internet hoaxes cyber awareness 2022.

Answers

There are a lot of fraudulent activates on online and it is very important to guide against them. There are strategies and online resources to help you identify and respond to a potential hoax.

First Identify that it is a hoax, Note that Hoaxes often booms where they are spread quickly and without consideration. If you notice or come in contact with a hoax through social media, the right thing to do thing to do is wait. The police or the school one is attending should issue a warning on the story.

Hoaxes are very common in the internet. Even with the recent digital technology, social media etc, a lot of spread of misinformation is now been spread at a faster and broader rate.

It is important that we as individuals, Parents and teachers be aware of the possibility that there may be shocking news about children and to known that the internet could be a hoax.  

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Which characteristics describe most nonmetals in the solid phase.

Answers

Solid nonmetals are generally brittle, with little or no metallic luster. Most nonmetals have the ability to gain electrons easily. Nonmetals display a wide range of chemical properties and reactivities.

Which of these contributed the most to the florida land boom.

Answers

Answer:

Florida land boom which was in the year 1920 was termed as the first real estate bubble which was in the Florida.

This bubble busted which left back remains of failed development projects and new cities for example, Aladdin city which is in the southern part of Miami-dade country and Miami Isola di Lolando.

The result of Florida's land boom created many cities out of Everglades and shaped Florida for many years.

During that time of land boom the prices on speculation were raised and development and land boom ensued.

Explanation:

Answer:

It is B they were able to travel to Florida for the land

Explanation:

Completa en tu cuaderno la siguiente rutina de pensamiento sobre la importancia de la nutrición.

Answers

Una nutrición balanceada es fundamental para mantener un estado saludable. Dicha nutrición se puede lograr incorporando macronutrientes y micronutrientes en cantidades adecuadas.

La nutrición se refiere al acto de ingerir alimentos para mantenerse en un estado saludable tanto físico como mental (y emocional).

Una alimentación saludable comprende la ingesta de macronutrientes, es decir, proteínas, lípidos, y carbohidratos, como así también micronutrientes tales como vitaminas y minerales.

Cada uno de estos nutrientes debe ser ingerido en cantidades adecuadas de acuerdo a las características fisiológicas del individuo, es decir, de acuerdo a su peso, edad, altura, etc.

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It is estimated that __________ percent of adults in the united states have a cell phone.

Answers

Cellphone consumption in the United States is such that the percentage of adults with a cell phone is 90%.

Cellphone ownership in the United StatesMore than 90% of its citizens owning a cell phone. More than 200 million adults owning a smartphone.

The United States therefore has one of the highest adult cellphone ownership rates in the world which is made easier by the packages offered by cellphone companies and networks.

In conclusion, 90% of American adults own a cell phone.

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The perimeter of the figure below is 133.1 ft.
Find the length of the missing side.

Answers

Answer:

9.6

Explanation:

because if we did if we subtract the total number which is which we are giving 133.1 minus the total number is that the Debt term give us by him by the drawing it will give us 9.6 feet

9.6 ft because if you add all the sides then subtract by the actual perimeter then you get x= 9.6 ft

What caused the february revolution of 1917 brainly.

Answers

Answer:

Russia disastrous involvement in world war l

This is the immediate cause of the February Revolution

Why there's no place like home for the holidays commonlit answers.

Answers

People often looks forward to holidays. Why there's no place like home for the holidays is due to different reasons such as;

Christmas rituals where everyone come together and have a nice time.The home serves as an anchor of order and comfort.The home is  safe, warm and a comforting place to be.

Why there's no place like home for the holidays  is a very significant and important text by Frank T. McAndrew. This was written in 2017 to show the significance of the home. The physical surrounding often influences a man's life.

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Which of the following best describes the maya civilization?.

Answers

Answer:

It is connected directly to the Mayan government.

Explanation:

The Mayan religion was a polytheistic religion. Religious leaders were at the top of their social hierarchy. They had many rituals to honor and worship their ancestors as they believed they were the ones who interceded for the living ones.

An event with a probability of 0 is an event with a probability of 1 is.

Answers

Answer:

An event with a probability of 0 is Impossible. ✔

An event with a probability of 1 is Certain. ✔

Hope I have  Helped ❤

The aachen gospels of otto the third manuscript. Christ is washing his apostles feet in front of a large building. The aachen gospels of otto iii, part of which is shown above, is an example of what kind of manuscript?.

Answers

Answer:

It is an Ottonian manuscript. It produced magnificent medieval illuminated manuscripts and it is about religion. They were a major art form of the time, and monasteries received direct sponsorship from emperors and bishops, having the best in equipment and talent available. The range of heavily illuminated texts was very largely restricted (unlike in the Carolingian Renaissance) to the main liturgical books, with very few secular works being so treated.

Explanation:

Answer:

An Ottonian manuscript.

Explanation:

Edge 2022

Among the top motivators driving corporations to engage in csr include all of the following reasons except.

Answers

There are different types of motivating factors. Among the top motivators driving corporations to engage in CSR include all of the following reasons except Meeting or exceeding budget.

Budget meetings is simply known as a vital  meeting mainly for smaller businesses and large corporations.

These meetings are mostly held so as to talk about budget planning, the operating of budget and the various changes need to be made to the budget so as to achieve organization's goal.

There are different motivating factors aimed at increasing shareholder value and reputation management through the means of CSR reporting. Values-driven factors are known to be the most important motivators.

See full question below.

Among the top motivators driving corporations to engage in CSR include all of the following reasons EXCEPT:

Select one:

a. Meeting or exceeding budget

b. Ethical considerations

c. Innovation and learning

d. Employee motivation

a. Meeting or exceeding budget

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What type of fallacy does this argument represent? hasty generalization ad populum begging the claim genetic fallacy.

Answers

Answer:

The answer is A: hasty generalization

Explanation:

Got 100% on the quiz

Answer:

A

Explanation:

there are 80 students in a school every student is taking either algebra or pre calculus

Answers

Answer:

Is that Real or a question

tell me pls

Which of the following best describes the meaning of "force"?.

Answers

Answer:no no no no no no

Explanation: yes yes yes yes yes

(mc)for which of the following strategic reasons did the united states acquire the midway islands? to spread christian and democratic ideals to the citizens living in the south pacific to build naval protection against rivals as the united states increased trade with asia and latin america to increase overseas trade to keep the country’s economy strong following a severe depression to slow the spread of asian countries’ influence in the pacific islands.

Answers

The reason the United States acquired the Midway Islands was to build naval protection against rivals as the United States increased trade with Asia and Latin America.

The Midway Islands:

Were the first territories in the Pacific that the U.S. acquired. Came under the administration of the U.S. Navy.

With the U.S. Navy controlling the islands, we can therefore say that the U.S. acquired the islands as a means of navy protection for American trade in Asia and related areas.

In conclusion, option B is correct.

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Answer:

to build naval protection against rivals as the United States increased trade with Asia and Latin America

Explanation:

I got it right on the test.

Where would you go to find all the lists you can use to fill in forms in quickbooks online?.

Answers

Answer:

O Go to the Gear icon select All Lists O Go to the Plus icon and choose All Lists O Go to the Accounting screen and select All Lists O Go to the Reports screen and select All Lists

Explanation:

Hope this helps!!

Itz Deepika Here to help ~

Note:- If you have any more questions then let me know .

Homework = Use Comment section

The key financial consideration in choosing between private and 3pl distribution options is.

Answers

A key (important) financial consideration that must be considered when choosing between private and third-party logistic provider (3PL) distribution options is: the volume (quantity) of product being moved.

Supply chain management (SCM) can be defined as the effective and efficient management of the flow of products (goods) and services from the manufacturers (producers) to the consumers in a timely manner.

Generally, there are different types of service providers in the supply and logistics chain management and they include:

Private distributorsCommon (public) carriersContract carriersFreight forwardersThird-party logistic provider (3PL)

A third-party logistic provider (3PL) refers to a service firm that is saddled with the responsibility of handling all the logistics requirements of other business firms.

Ideally, a key (important) financial consideration that must be considered when choosing between private and third-party logistic provider (3PL) distribution options is the volume (quantity) of product that is being moved to the market.

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Factual information can be presented with bias. Please select the best answer from the choices provided t f.

Answers

Answer:

False

Explanation:

When giving factual information it is important to be able to present your views without bias. When receiving the information it is important to be able to distinguish bias from fact.

Answer:

right

Explanation:

Which of the following graphs could be the graph of the function f(x) = x3 + 8? mc019-1. Jpg mc019-2. Jpg mc019-3. Jpg mc019-4. Jpg.

Answers

Functions can be represented using equations, graphs and tables.

The graphs are not given.

So, we simply plot the graph of the given function.

The function is given as:

[tex]f(x) = x^3 + 8[/tex]

When x = 1, we have:

[tex]f(1) = 1^3 + 8[/tex]

[tex]f(1) = 9[/tex]

When x = 2, we have:

[tex]f(2) = 2^3 + 8[/tex]

[tex]f(2) = 16[/tex]

When x = 3, we have:

[tex]f(3) = 3^3 + 8[/tex]

[tex]f(3) = 35[/tex]

When x = 4, we have:

[tex]f(4) = 4^3 + 8[/tex]

[tex]f(4) = 72[/tex]

Represent the above results as a table, we have:

x          f(x)

1          9

2         16

3          35

4          72

See attachment for the table of [tex]f(x) = x^3 + 8[/tex]

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Which of the following scales is the key of c major.

Answers

There are different scales in music. The C major (or the key of C) is known to be a major scale that is often based on C. It is made up of different pitches C, D, E, F, G, A, and B.

C major is simply known to be one of the most user key signatures found in music. It is known to have its key signature to have no flats and no sharps keys.

The C major scale is known to have the scale of zero sharps or flats. It does not have any key signature and it makes it easier to identify any music in the key of C major.

For one to be able to play the C major scale ascending, one must start with the root note C and play the notes in order: C - D - E - F - G - A - B - C. Then, one can either go right back down the scale of B - A - G- F- E - D.

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A person is watching a boat from the top of a lighthouse.

Answers

Answer:

no way!!!!!!!!!!!!!!!!!

Explanation:

The quote below was written in the 1920s: the disaster which was impending was destined to be as bewildering and frightening to the rich and the powerful and the customarily sagacious as to the foolish and unwary holder of fifty shares of margin stock. --frederick lewis allen source: http://xroads. Virginia. Edu/~hyper/allen/ch13. Html to what event does this quote refer? the events on black tuesday the programs of the first new deal the dust bowl the end of the dust bowl.

Answers

Answer:A the events of black teusday

Explanation:

Answer:

I think that it's c: the dust bowl

Explanation:

Eight less than four times a number is less than 56.

Answers

Answer:

depending on the number I think I could be wrong not 100%

According to research by fergus i. M. Craik and endel tulving on levels of processing, which of the following would most improve the ability to recall the word "umbrella"?.

Answers

According to the levels of processing, deciding whether an umbrella would be useful to pack for a trip, would most improve the ability to recall the word "umbrella". This model focuses on the depth of processing in memory.

The 'levels of processing' is a model developed by the cognitive psychologists F. Craik and R. Lockhart in 1972.

This model (levels of processing model) puts focus on the depth of processing developed for memory tasks.

This model can be used to predict how information is processed, where memory can be considered as an outcome of processing information.

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What would happen to crabtree if he was ever late to work? he would lose his wages. He would get in trouble with his parents. He would be beaten. He would be fired.

Answers

Answer:

he would be beaten

Explanation:

He would be beaten if he was ever late to work. Therefore option C is correct.

What are Parents?

It would seem simple to define the term "parenting" as follows: Parenting is the act of nurturing, supporting, encouraging, directing, guiding, and loving a child or children from infancy to adulthood.

Consistency and routine are key components of good parenting, which provides kids with a sense of control. Redundancy becomes the goal for parents because good parenting emphasizes helping children become independent. A style of parenting that takes into account the age and developmental stage of the kid is good parenting.

The biological parents of a kid are typically the father and mother whose DNA the child carries. Although they do not need to be blood relatives, legal parents have a family link to the kid by law, such as in the case of an adopted child.

Hence, He would be beaten if he was ever late to work.

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Other Questions
yes that. Read the excerpt below and then answer the question that follows:The Book of DragonsChapter III The Deliverers of Their Country, an excerptBy E. NesbitIt all began with Effie's getting something in her eye. It hurt very much indeed, and it felt something like a red-hot sparkonly it seemed to have legs as well, and wings like a fly. Effie rubbed and criednot real crying, but the kind your eye does all by itself without your being miserable inside your mindand then she went to her father to have the thing in her eye taken out. Effie's father was a doctor, so of course he knew how to take things out of eyes.When he had gotten the thing out, he said: "This is very curious." Effie had often got things in her eye before, and her father had always seemed to think it was naturalrather tiresome and naughty perhaps, but still natural. He had never before thought it curious.Effie stood holding her handkerchief to her eye, and said: "I don't believe it's out." People always say this when they have had something in their eyes."Oh, yesit's out," said the doctor. "Here it is, on the brush. This is very interesting."Effie had never heard her father say that about anything that she had any share in. She said: "What?"The doctor carried the brush very carefully across the room, and held the point of it under his microscopethen he twisted the brass screws of the microscope, and looked through the top with one eye."Dear me," he said. "Dear, dear me! Four well-developed limbs; a long caudal appendage; five toes, unequal in lengths, almost like one of the Lacertidae, yet there are traces of wings." The creature under his eye wriggled a little in the castor oil, and he went on: "Yes; a bat-like wing. A new specimen, undoubtedly. Effie, run round to the professor and ask him to be kind enough to step in for a few minutes.""You might give me sixpence, Daddy," said Effie, "because I did bring you the new specimen. I took great care of it inside my eye, and my eye does hurt."The doctor was so pleased with the new specimen that he gave Effie a shilling, and presently the professor stepped round. He stayed to lunch, and he and the doctor quarreled very happily all the afternoon about the name and the family of the thing that had come out of Effie's eye.But at teatime another thing happened. Effie's brother Harry fished something out of his tea, which he thought at first was an earwig. He was just getting ready to drop it on the floor, and end its life in the usual way, when it shook itself in the spoonspread two wet wings, and flopped onto the tablecloth. There it sat, stroking itself with its feet and stretching its wings, and Harry said: "Why, it's a tiny newt!"The professor leaned forward before the doctor could say a word. "I'll give you half a crown for it, Harry, my lad," he said, speaking very fast; and then he picked it up carefully on his handkerchief."It is a new specimen," he said, "and finer than yours, Doctor."It was a tiny lizard, about half an inch longwith scales and wings.So now the doctor and the professor each had a specimen, and they were both very pleased. But before long these specimens began to seem less valuable. For the next morning, when the knife-boy was cleaning the doctor's boots, he suddenly dropped the brushes and the boot and the blacking, and screamed out that he was burnt.And from inside the boot came crawling a lizard as big as a kitten, with large, shiny wings."Why," said Effie, "I know what it is. It is a dragon like the one St. George killed."And Effie was right. That afternoon Towser was bitten in the garden by a dragon about the size of a rabbit, which he had tried to chase, and the next morning all the papers were full of the wonderful "winged lizards" that were appearing all over the country. The papers would not call them dragons, because, of course, no one believes in dragons nowadaysand at any rate the papers were not going to be so silly as to believe in fairy stories. At first there were only a few, but in a week or two the country was simply running alive with dragons of all sizes, and in the air you could sometimes see them as thick as a swarm of bees. They all looked alike except as to size. They were green with scales, and they had four legs and a long tail and great wings like bats' wings, only the wings were a pale, half-transparent yellow, like the gear-boxes on bicycles.Based on the rising action in the bolded paragraphs, what do we know about Daddy? 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WILL MARK BRAINLYIST can someone please help me on this all u have to do is search up on the internet and then put down 4 facts that are mentioned in the web site and give the main idea to but make sure I know were the main idea is web site: should we bring back extinct species xyz company's cost function for the next four months is c=500000+5q then a) find the be dollar volume of sales if the selling price is br. 6/unitb) what would be the company's cost if it decides to shutdown operations for the next four months 10 miles per hour is an example of an objects what? Suppose DEF has an exterior angle at vertex D. The measure of the exterior angle is (8x2), mE=(3x8), and mF=(4x+13). What is the measure of the exterior angle at vertex D?A. 7B. 13C. 41D. 54 PLEASE HELP! ILL GIVE BRAINLIEST!I! I uploaded a picture below. how I can answer this question, NO LINKS, if you answer correctly I will give u brainliest! lines 1-7 what idea is the author mostly likely to explore in his essay, based on the conversation between the author and his female friend