Prove the following identity


sin x(sec x+cscx)= tan x +1

Answers

Answer 1

Answer:

Step-by-step explanation:

________________________________________________________

FACTS TO KNOW BEFORE SOLVING :-

[tex]\sin x = \frac{1}{cosec \: x} \: \: or \: \: cosex \: x = \frac{1}{\sin x}[/tex][tex]\cos x = \frac{1}{\sec x} \: \:or \: \: \sec x = \frac{1}{\cos x}[/tex][tex]\tan x = \frac{\sin x}{\cos x}[/tex]

________________________________________________________

In the question ,

L.H.S. = [tex]\sin x (\sec x + cosec \: x)[/tex]

R.H.S. = [tex]\tan x + 1[/tex]

Lets solve L.H.S. first.

[tex]\sin x (\sec x + cosec \: x)[/tex]

[tex]=> \sin x( \frac{1}{\cos x} + \frac{1}{\sin x} )[/tex]

[tex]=> \frac{\sin x}{\cos x} + \frac{\sin x}{\sin x}[/tex]

[tex]=> \tan x + 1[/tex]

∴ L.H.S. = R.H.S. (Proved)


Related Questions

Classify the solid figure.
O A. rectangular prism
O B. rectangular pyramid
O C. cylinder
O D. quadrilateral
HELP MEEE

Answers

That looks like a rectangular prism
It’s A.
..................

Amelia earned $100 on a $1000 investment with a bank for a 3-year term. what rate did the bank offer her?

Answers

Answer:

3.33%

Step-by-step explanation:

Rate = 100xSI / PxT

P = 1000

SI = 100

T = 3

Rate = 100 x 100 / 1000 x 3 = 3.33%

help me please anyone here? will mark brainliest of correct but report if nonsense​

Answers

Step-by-step explanation:

1/(1 - p + p²) - 1/(1 + p + p²) - 2p/(1 - p² + p⁴) =

[ (1 + p + p²)-(1 - p + p²)/(1 - p + p²)(1 + p + p²) ] - 2p/(1 - p² + p⁴) =

2p/(1 + p + p² - p - p² - p³ + p² + p³ + p⁴) - 2p/(1 - p² + p⁴) =

2p/(1 + p² + p⁴) - 2p/(1 - p² + p⁴) =

[ 2p(1 - p² + p⁴) - 2p( 1 + p² + p⁴) ]/(1 + p² + p⁴)(1 - p² + p⁴) =

(2p - 2p³ + 2p⁵ - 2p - 2p³- 2p⁵) / (1 - p² + p⁴ + p² - p⁴ + p⁶ + p⁴ - p⁶ + p⁸) =

-4p³ / (1 + p⁴ + p⁸)

If you roll a 6-sided die 54 times, what is the best prediction possible for the number of times you will roll a one?

Answers

Answer:

50% of the time (27 times) you will get an even number

Step-by-step explanation:

sorry if it wrong

Mr. Johnson sold a new tv that was $450. If he earns 7% commission, how much money will he make in commission?

Answers

Answer:

$31.50

Step-by-step explanation:

can someone send me a random receipt you have you gotten recently. it can be anything at all pls​

Answers

is this for fetch rewards

1) You have three- fourths yards of pipe. How many pieces can you cut the pipe into if each piece is one-eighth yard?

Answers

Answer:

Step-by-step explanation:

(3/4)/(1/8)

(3/4)(8/1)

24/4

6 pieces of pipe

Find the circumference of the circle.

Answers

Answer:

the 3rd one 72.22 is the answer

Answer:

the formula for it is 2*3.14*r

so to get the radius you divide the diameter by two, so 23 divided by 2 is 11.50

so then we do 2*3.14*11.50= 77.22

there u go!

Step-by-step explanation:

Find X please help me with test corrections due midnight tonight!
If HBN is congruent to LYR.

Answers

Answer:

the answer is

x=22..........

2. A local t-shirt company sold 2000 t-shirts two weeks ago when they charged $10 for each shirt. The following week they sold 1120 t-shirts when they raised the price to $19 per shirt. Assuming that this rate of change continues find the following: a. Find a linear function S(p) that models the number of shirts sold as a function of the price p. b. Explain the meaning of the slope In terms of the problem. c. Predict the number of shirts the store would sell if they charged $25 for each shirt. d. If the store would like to maintain a weekly sales level of 1450 shirts how much should they charge per shirt?

Answers

9514 1404 393

Answer:

  a) S(p) = -97.78p +2977.78

  b) about 98 fewer shirts per week will be sold for each $1 increase in price

  c) 533 shirts per week

  d) $15.63

Step-by-step explanation:

a) You are given two ordered pairs: (p, s) = (10, 2000) and (19, 1120). The two-point form of the equation for a line can be used.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  s = (1120 -2000)/(19 -10)(p -10) +2000

  s = -97.78(p -10) +2000

  S(p) = -97.78p +2977.78

__

b) The slope is shirts/dollar, meaning about 98 fewer shirts will be sold for each dollar increase in price.

__

c) S(25) ≈ 533

At a price of $25, the store would sell about 533 shirts per week.

__

d) 1450 = S(p) = -97.78p +2977.78

  -1527.78 = -97.78p

  15.625 = p ≈ 15.63

The store should charge $15.63 per shirt to maintain sales of 1450 shirts per week.

How many more people studied for 0-30 minutes than people who studied for 121-150 minutes?

Answers

Answer:

5 more people studied more in 0-30 minutes than people who studied 121-120 minutes.

Step-by-step explanation:

five more people studied for 30 minutes then 121 minutes

HELP PLEASE PLEASEEEEEE

Answers

Answer:

I think the area is 9 ft square

Entomologists estimate that an average person consumed almost a pound of bug parts each year. There are that many insect eggs, larvae, and miscellaneous body pieces in the food we eat and the liquids we drink. The Food and Drug Administration (FDA) sets a Food Defect Action Level (FDAL) for each product. For example, the legal limit for peanut butter is 30 insect fragments per 100 grams. You just bought the crackers with 25 grams of peanut butter. What is the probability that the snack will include at least 3 crunchy critters

Answers

Answer:

0.9797

Step-by-step explanation:

We have X = number of insects in the 25bgrams of butter

Then the legal limit of concentration in peanut butter = 30 fragments/ 100 grams

Then insect amount in 25 grams =

E(X) = 30/100 x 25

= 0.3 x 25

= 7.5 fragments of insects

Using the poisson function in Excel, the probability of at least 3 crunchy critters

1 - p(X<=2)

p(X<=2) = POISSON (2, 7.5, TRUE) = 0.020156715

1 - 0.020156715

= 0.9797

Is the relationship between the number of days and the number of hours proportional?

Answers

Answer:

yes because no matter what 24 hrs will equal a day

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

If I save 10$ at the end of every month for 12 years how much will I have ?

Answers

Answer:

1440

Step-by-step explanation:

theres 144 months in 12 years and I just multiplied it by 10

Find the missing side. Round to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

1)

Hyp =40

∠48

x = Adj

use CAH since it's got these pieces in it

Cos(48) = x / 40

40* Cos(48) = x

26.76522 = x

x = 26.8  ( rounded to nearest 10th)

2)

∠29

Hyp = 35

Opp = x

use SOH since this problem has those pieces in it

Sin(29) = x / 35

35*Sin(29) = x

16.9683 = x

x = 17.0  (rounded to nearest 10th)

3)

40 = Adj

∠16

Hyp = x

use CAH again

Cos(16) = 40 / x

x = 40 / Cos(16)

x = 41.611

x = 41.6 (rounded to nearest 10th )

4)

∠55

Opp = 35

x = Adj

use TOA

Tan(55) =35/x

x = 35/Tan(55)

x = 24.5072

X = 24.5  ( rounded to nearest 10th)

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(p, q) = 8qe−p + 4pe−q, (0, 0) maximum rate of change $$ Correct: Your answer is correct. direction $$

Answers

Answer:

Step-by-step explanation:

[tex]Given \ f (p,q) = 8qe^{-p} + 4pe^{-q} \ where \ P_o(0,0) \\ \text{thus the gradient of f is: } \\ \\ \bigtriangledown f(p,q) = \Big(\dfrac{\partial f}{\partial p}, \dfrac{\partial f}{\partial q} \Big) \\ \\ \dfrac{\partial f}{\partial p} = -8qe^{-p} + 4pe^{-q} \\ \\ \dfrac{\partial f}{\partial p} = 8qe^{-p} - 4pe^{-q} \\ \\ Then: \bigtriangledown f(p.q) = (-4qe^{-p}+ 8qe^{-q}, 4qe^{-p}- 8qe^{-q}) \\ \\ f(0,0) = (-4*(0)e^{-0}+ 8*(0)e^{-(0)}, 4*(0)e^{-(0)}- 8*(0)e^{-(0)}) \\ \\ = (0+8,4-0) = (8.4)[/tex]

[tex]\Big| \Big | \bigtriangledown f(0,0) = \sqrt{(8)^2+4^2} \\ \\ = \sqrt{64+16} \\ \\ = \sqrt{80}[/tex]

[tex]\mathbf{the \ direction \ of \ maximum \ change \ is }= \mathbf{\sqrt{80}} \\ \\ \mathbf{direction }(8,4)[/tex]

(Urgent) Worth 15 points 7.3

Answers

Answer: 20790

Step-by-step explanation:

Choose all that apply!! i’ll give a brainly!!

Answers

Step-by-step explanation:

The answer is A

PLEASE FOLLOW ME

Help needed ASAP!! I will give brainliest! (You don’t need to plot the graph)

Answers

Answer:

first one y: -3, 0, 3, 6, 12

second one y:5, 2, 0, 2, 5

Step-by-step explanation:

for the first one the equation is y=3x

so when it goes as x:-1, 0, 1, 2, 4

so you should multiply each number by 3 as the equation does

(just replace each number by x in the equation)

so y: -3, 0, 3, 6, 12

next one: equation is y=[tex]x^{2}[/tex]+1

so do the same as up there: replace x with every number

x:-2, -1, 0, 1, 2

so y will be

y:5, 2, 0, 2, 5

The millers are going to put a pool in their backyard this summer. The pool will have a depth of 5 feet, and the dimensions shown in the picture. What will be the total volume of water needed to fill the pool?

Answers

Answer:

D : 510 units

Step-by-step explanation:

NOTE:

Something to consider when solving problems like this is to break the large shape down into smaller, more managable shapes. So for this problem, you can break down this irregular shape into two rectangles. This will make solving problems similar to this easier in the future :)

WORK:

I broke down this shape into two rectangles with the following dimensions:

- 12 meters by 5 meters

- 3 meters by 14 meters

You also know that the depth has to be 5 feet (the problem itself did not account for differences in feet and meters, as when I converted the 5 feet to meters and solved that way, none of the answers were correct)

Using this information, you can now solve for the volume of each of the rectangles

12*5*5 = 300 units

3*14*5 = 210 units

Then, you simply add the two volumes together to find the total volume needed to fill the pool which equals

510 units


How many even numbers less than 1000 can be formed from the given
digits 0,2,3,5 if repetition is not allowed.
(a) 16
(b) 24
(c) 6
(d) none of these

Answers

Answer:

non of them it should be 32 iʻm pretty sure

Step-by-step explanation:

China and the United States are playing each other in the championship match of the 1999 Women's World Cup soccer tournament. Brandi Chastain of the U.S. team is about to take a penalty kick against the Chinese team's goalkeeper, Gao Hong. Chastain will kick the ball from 18 yards away from the goal at 120 miles per hour. How many seconds does the goalkeeper have to react, dive, and reach the ball before it crosses the goal line

Answers

Answer:

The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.

Step-by-step explanation:

We use the following relation to solve this question:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance, and t is the time.

Chastain will kick the ball from 18 yards away from the goal at 120 miles per hour.

Since the velocity is in miles per hour, the distance has to be in yards.

Each yard has 0.000568182 miles, so the ball will be kicked from 18*0.000568182 = 0.0102 miles.

This means that [tex]v = 120, d = 0.0102[/tex]

How many seconds does the goalkeeper have to react, dive, and reach the ball before it crosses the goal line?

We have to find t, first in hours. So

[tex]v = \frac{d}{t}[/tex]

[tex]120 = \frac{0.0102}{t}[/tex]

[tex]120t = 0.0102[/tex]

[tex]t = \frac{0.0102}{120}[/tex]

[tex]t = 0.000085[/tex]

An hour has 3600 seconds. So

3600*0.000085 = 0.306.

The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.

The equation of a line is shown.
6x – 3y = 5
A dilation centered at the origin with a scale factor of 6 is applied to this line.
A. What is the slope of the line after the dilation?
B. What is the value of the y-intercept of the line after the dilation?

Answers

Answer:

my guess would have to be

A. slope= 4      

B. y-intercept= 23/3 or 7  2/3(simplified)

Step-by-step explanation:

im not sure how accurate my answer would be but what i did was put the equation in slope intercept form and added 6 for the dilatation to all factors of the equation.

The slope is 2/3.

The y-intercept is -5/3.

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line.

6x - 3y = 5

Now,

To apply a dilation with a scale factor of 6 centered at the origin.

We multiply both sides by 6.

So,

6 (6x - 3y) = 6 x 5

Now,

Simplifying.

36x - 18y = 30

Dividing both sides by 18.

2x - y = 30/18

2x - y = 5/3

Now,

Writing in slope-intercept form.

y = mx + c

So,

y = 2x - 5/3

This means,

Slope m = 2

y-intercept c = -5/3

Thus,

The slope is 2/3.

The y-intercept is -5/3.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ6

pls help!due very soon.ill pick brainliest for the answer that helps me the most.(I can only pick brainliest if there's two answers)

Answers

1 : 3 because you have to add all the bulbs which equals 60, so it would be 20:60 since 20 is the Daisy bulbs and then you simplify

10 1/8 +2 1/4
Show work please
and no links

Answers

Step-by-step explanation:

Please refer to the attachment

I WILL MARK BRAINLIEST PLEASE ANSWER ( NO LINKS I WILL REPORT YOU IF YOU GIVE ME A LINK)

Answers

Answer: B

Step-by-step explanation:

WILL MARK BRAINLIEST
Hannah jumps rope 300 times. Sharon jumps rope 179 times. How many more times does Hannah jump rope than Sharon? Click on the numbers to enter the answers in the boxes​

Answers

Answer:

121

Step-by-step explanation:

300

-179

-------

121

Find the surface area of this cube Be sure to include the correct unit in your answer
i dont really understand this pls help me ill give you brainly and 5 stars and a heart

Answers

Answer:

Which cube?

Step-by-step explanation:

................

what isnithegdierhfdirhfduidhfvuc

Answers

hi, im chelsea. whats your favorite dinner food?

Answer:

it's cuvfhdiudfhridfhreidgehtinsi tahw

Step-by-step explanation:

have a good day

Other Questions
help a girl outtttt please HELP PLEASE!!!!Bellwork: Verbs Definition: Often the verb is the action word in the sentence. It defines the action. The verb be and its forms (was, were, are, is, am) do not really show action but a state of being or relationship between the subject and what follows the verb be (Lab tutors are helpful). The verb may consist of one word, or the main verb may contain one or more helping words. Some helping words are has, am, were, might, should, must, are, be . . . Examples: Whole group instuctionThe man screamed loudly. (What did the man do? He screamed.) All the men have been screaming. (What were the men doing? They have been screaming.) All the men were old. (The adjective old is linked to the subject of men.) Exercises: Directions: Underline the verb (or verb phrase) in the following sentences. 2. There are over a thousand millimeters in a yard. 4. Gold melts at 1,063 degrees Centigrade. 6. The George Washington Bridge is located between New York and New Jersey. 8. Automobiles have been crossing it since 1931. 10. It is constantly being painted. 12. It is over 150 years old since it was established in 1802. 14. Many visitors go to West Point and watch the dress parade on Saturdays. Activity 1) Complete part 4 and 5 of i-ready toolboxDI i-ready and CommonlitAssignment needs to be complete - do research and write National Campaign to Stop Violence essay competition entitled: "Do the Write Thing Challenge."You are writing an essay to explain how violence has impacted their lives and how violence in the U.S. can be reduced. The information provided may be a fictional or real account. Be sure to do research when responding to this work. o Do not write/type your name, id number or school information on the actual essayo If your submission is fictional, please write that on the top of the entryo Only submit one copy of the essayo Cover sheet must be either typed or printed in legible handwriting in ink only (The title Do the Write Thing Challange, your name, Ms. Hidalgo, Period #, and YWPAResearch question: How does violence impact society today in the US?HELP PLEASE!!!! 2 people can paint a fence in one hour How long would it fake 10 people? What was the purpose of the emancipation Proclamation? How were contrabands different from other african americans who joined the Union army? HELP WILL GIVE BRAINLIEST!!! NO LINKS PLS English essay about :what goes around comes around SOME ONE HELP PLEASE In the letter "Letter from Birmingham jail", what does the word tension mean? An editor gets $2890 raise each year. In her eighth year, she is making $27,400 per year. Write a function that represents her income after x years she has worked at the company If the graph of the second equation in the system passes through the points (-12, 20) and(4, 12), which statement is true? For what value of m is the expression x4+mx2+64 a perfect square? Select all the equations that are true: Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length. what is the pandemic can someone help find me? i need to answer!!!! work out m and c for the line y= 2x+1 El punto ms alto de un repetidor de televisin situado en la cima de una montaa se ve desde un punto del suelo p bajo un ngulo de 67 si nos acercamos a la montaa 30 metros lo vemos bajo un ngulo de 70 y desde ese mismo punto vemos la cima de la montaas bajo un ngulo de 66 . Calcular la altura del repetidor. UHMM I REALLY NEED HELP IM BAD AT Science The table below shows the favorite color of all the students at Wolff Elementary school. Your at a sandwich shop, they offer 3 types of breads, 4 types of meats, and 8 types of toppings. How many different combinations are there?