) f) 1 + cot²a = cosec²a​

Answers

Answer 1

Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

[tex]\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}[/tex]

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

[tex]\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}[/tex]

Another identity is:

[tex]\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}[/tex]

Therefore:

[tex]\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}[/tex]

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

[tex]\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}[/tex]

Another identity:

[tex]\displaystyle \large{\sin^2x+\cos^2x=1}[/tex]

Therefore:

[tex]\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}[/tex]

Hence proved, this is proof by using identity helping to find the specific identity.


Related Questions

An education website has 434,206 daily unique visitors. An e-commerce website gets double the number of visitors. How many visitors does the e-commerce website get? Show Your Work

Answers

Answer:

868412

Step-by-step explanation:

434206x2=868412

The function P(t)=25,000(1.1023)t2 can be used to model the population in the town of Madison t years from now. Interpret the function in terms of the context for this situation.

Answers

Answer:

A growth function has the following form.

where  = Original amount,

r = annual rate of change,

n = number of periods,

t = time in years

Since the time is in years, we need to convert t into days. We know that 1 year = 365 days. So t years = 365t days.  

So in this case, n = 365, r = 0.0095.

Then the function is rewritten as follows.

The daily growth rate would be  

Step-by-step explanation:

t=number of years

Lets find year wise population for example

let years be 3t=3

[tex]\\ \sf{:}\longrightarrow P(3)=25,000(1.1023)3^2[/tex]

[tex]\\ \sf{:}\longrightarrow P(3)=27557.5(9)[/tex]

[tex]\\ \sf{:}\longrightarrow P(3)=248017.5[/tex]

The sum of Ellie's age and Genya's age is 60. In sex years, Genya will be eight times older than Ellie will be. How old is Ellie now?

Answers

Answer:

ellie is 2 and genya is 58, explanation in picture attached

can someone please help with math?!

Answers

Slope: 3/5
The formula for slope is rise over run
In this case the rise would be Positive three because the points went from -2 to positive one. And the run would be 5 because it goes from -1 to 4
Hope this helps!!
Please tell me if I have made a mistake, I enjoy learning from them:)

RS is the perpendicular bisector of TU. Find x and y​

Answers

Answer:

x = 1

y = 30°

Step-by-step explanation:

is RS is ⊥ to TU then TS = US so we can use this equation to find 'x':

20x-3 = 5x+12

15x = 15

x = 1

we also know that RS intersecting with TU creates a 90° angle

if 3y = 90 then y = 30

Eva is flying a kite, holding her hands a distance of 2.75 feet above the ground and
letting all the kite's string play out. She measures the angle of elevation from her
hand to the kite to be 25°. If the string from the kite to her hand is 130 feet long, how
many feet is the kite above the ground? Round your answer to the nearest tenth of a
foot if necessary.

Answers

Answer: 57.7 feet above the ground

sin 25= opposite/hypotenuse

 = x/130

130 sin 25 = x

x=54.940374

54.940374+2.75 = 57.7

 

u +7 at u=9 step by step explanation plus answer i really need to know how please

Answers

Answer: 16

u=9 so we can plug 9 into the equation.

9 + 7 = 16

Select True or False to correctly classify each inequality.
Inequality True or False ( will give brainliest)

−2≤−2 true or false
6.1<6.1 true or false
5.6≥5.6 true or false
5.6≥5.6 true or false
−4>4 true or false

Answers

Answer:

−2≤−2 True

6.1<6.1 False

5.6≥5.6 True

5.6≥5.6 True

−4>4  False

Step-by-step explanation:

Hence,  all the statements are true except option (4).

What is the inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Here given that,

[tex]-2\leq -2[/tex] is true, because [tex]-2[/tex] is equals to each other.

[tex]6.1 < 6.1[/tex] is true, because [tex]6.1[/tex] is equals to each other.

[tex]5.6\geq 5.6[/tex] is true, because [tex]5.6[/tex] is equals to each other.

[tex]5.6\geq 5.6[/tex] is true, because [tex]5.6[/tex] is equals to each other.

[tex]-4 > 4[/tex] is false, because [tex]-4[/tex] is not greater than [tex]4[/tex].

Hence,  all the statements are true except option (4).

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Which angle do ΔEBC and ΔADC share?




Answers

Answer:

The angle in C

Step-by-step explanation:

simplify 4 (5x+3)-4x

Answers

Answer:

16x + 12

Step-by-step explanation:

20x + 12 - 4x

20x - 4x = 16x

16x + 12

Answer: 15x + 12

Step-by-step explanation:

(4 x 5x). (4 x 3). (20x - 4x). 15x + 12 is your answer.

Write an expression for 5 times the difference of twice a number and 4

Answers

Answer:

1. 50-x

2. 2x+189

3. x+109

4. x+99

5. x*(76-39)

6. 75+x

7. 45-3x

8. 2x+15

9. 3x-25

10. x*(x+88)

Step-by-step explanation:

(7*10 to the power of 5)*(3*10 to the power of 2)

Answers

Step-by-step explanation:

do you mean

7×10⁵ × 3×10²

as you can see, these are all multiplications. and we can do in a first step the multiplications that combine the factors with the same exponent base or simple constants :

7×3 × 10⁵×10² = 21 × 10⁷

in what format do you need the result ?

21 × 10⁷

2.1 × 10⁸ (standard format)

210,000,000

A file that is 261 megabytes is being downloaded. If the download is 17.1% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.

Answers

Answer:

44.6 megabytes

Step-by-step explanation:

If 261 megabytes = 100% and we are looking for 17.1% then we can make a cross product.

261= 100

? = 17.1

It means that (17.1x261)/100 = 44.631

If we round our answer it equals 44.6

please help me!

ty :)

Answers

Answer:

slope: -4

Step-by-step explanation:

the formula to finding slope using two points is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

so insert the x- and y- values into the formula. you'll get:

[tex]m=\frac{-11-9}{3-(-2)}=\frac{-20}{5}=-4[/tex]

Jane’s starting annual salary is $45,520. At the beginning of each new year, she receives a $1,580 raise. What will her salary be after 11 years?

Answers

Answer:

$62,900

Step-by-step explanation:

Choose the point-slope form of the equation below that
epresents the line that passes through the points (-6, 4) and (2,
0). (2 points)

•y -4= - 1/2 (x+6)

•y-4= 2(x+6)

•y+6= - 1/2(x-4)

•y+6= 2(x-4)

Answers

Answer:

A) y-4=-1/2(x+6)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(0-4)/(2-(-6))

m=-4/(2+6)

m=-4/8

simplify

m=-1/2

y-y1=m(x-x1)

y-4=-1/2(x-(-6))

y-4=-1/2(x+6)

What common side does ΔABC share with ΔADC?


BC

AD

BD

AC


Answers

I think it’s AC, but I may be wrong

Answer:

it's a and c

luk closely

Here's the Question ~

[tex] {2 - 1}^{2} [/tex]

Answers

Answer:

The answer is 1

Step-by-step explanation:

1² = 1×1

= 1

2 - 1² = 2 - 1

= 1

Which expression is equivalent to 9 x 9 x 9 + 12 x 12 x 12?

Answers

Answer:

i think probably 2457 is answer

137x723+462x50=?


do yall think its ok for your girl to k.i.s.s. other people?
and would yall let it slide and think it was a joke?

Answers

Answer: 122151no it is not okay for someone to do that behind the person their datings back honestly. i have had this happen to me by one of my ex boyfrie.nds and it does bother me that i let him hur.t me like that but no it isnt okay and you should never let it slide cause they could always do it again.

5) - 2y = -2x

slope intercept form please someone help i don’t have much time

Answers

[tex]\text{Given that,}\\\\-2y = -2x\\\\\implies y = x\\\\\implies y = x+0\\\\\\\text{This is the slope- intercept form(y=mx+b) of the given equation,}\\ \text{where the slope is 1 and y - intercept is 0.}[/tex]

Please help meeeeeeee! Gratefully appreciate it, happy holidays!

Answers

Answer:

x = 50

Step-by-step explanation:

180-(50+80)=x

180-130=50

Any help wit this one

Answers

Answer:

22.5 centimetres per second.

Step-by-step explanation:

To get the awnser for this you do the highest length of centimetre which is 90 divided by how many seconds it took to get to 90 centimetres, then we do 90÷4 which equals to 22.5, so the awnser is 22.5 centimetres per second. Hope this helps.

There are 20 questions on a test. Three points are awarded for a correct answer and – 1 for an incorrect answer. If Brian answered 14 questions correctly and 6 incorrectly, what is his score?

Answers

Answer:

36 points

Step-by-step explanation:

3x14 = 42

1x6 = 6

42-6 = 36

Hope that helps

Answer:

54 hope this helps

the LCM and GCF of 66 and 101

Answers

Answer:

GCF: 1

LCM: 6,666

Step-by-step explanation:

I hope this helps!

Kiran and Mai are going on a long bike ride.
• Kiran can ride 4 miles every 16 minutes.
Mai can ride 4 miles every 12 minutes.
.
How long will it take each rider to reach the end of a 12-mile bike path?
1) It will take Kiran minutes to reach the end of a 12-mile bike path?
2) It will take Mai
minutes to reach the end of a 12-mile bike path?
Blank 1:
Blank 2:
Question 4 (2 points)

Answers

Answer:

kiran will take 48 minutes 16 x 3

mai will take 36 minuttes 13 x 3

Step-by-step explanation:

(1) Kiran will take 48 minutes to reach the end of a 12-mile bike path.

(2) Mai will take 36 minutes to reach the end of a 12-mile bike path.

What is ratio?

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Kiran rides 4 miles every 16 minutes.

Also, Mai rides 4 miles every 12 minutes.

To find the time taken by Kiran and Mai to reach 12 mile bike paths,

Use ratio property,

Time taken by Kiran to ride 4 miles = 16 minutes,

For 1 mile = 4 minutes,

For 12 miles = 12 x 4 = 48 minutes

Time taken by Mai to ride 4 miles = 12 minutes,

For 1 mile = 3 minutes

For 12 miles = 12 x 3 = 36 minutes.

Kiran will take 48 minutes and Mai will take 36 minutes to reach the end of a 12-mile bike bath.

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What does it mean by domain and range and how would I use that to fill out the table?​

Answers

The domain is the set of all allowed x values. In this case, we consider the whole numbers between 0 and 10. So we have x = 0, x = 1, x = 2, ... all the way up to x = 10.

To find the y values, you replace each x with the numbers mentioned and simplify.

For instance, if x = 2, then,

f(x) = 3.50x

f(2) = 3.50*2

f(2) = 7

This tells us that x = 2 packages cost y = 7 dollars.

domain is the x value, range is the y value. you cant have any duplicates. so if your table was (5,3) (6,3) (1,9) (5,7)
the domain would be 5,6,1 the range would be 3,9,7 you can repeat them if there is the same number in the range and the domain. for example (5,3) and (3,9) you would put 5 and 3 as the domain and 3 and 9 as the range. the range is the second number, the domain is the first in an ordered pair

help pls please hmmm​

Answers

Step-by-step explanation:

Here is your answer

(2)⁴*³2¹²

Answer:

2^12

Step-by-step explanation:

Since 2^4 is already powered you will only power the 4 and not the 2

For example (a^2)^3 = a^6

and not a*a*a^6

You only power the 2 and not the "a"

Hope this helps!

please solve quickly

Answers

Step-by-step explanation:

a

Volume = length ×width × height

therefore

5cm× 6cm×2cm=volume

60cm³= volume

the volume is 60cm³

b

Volume = length ×width × height

1200mm³=20mm×10mm×H

1200mm³=200mm²×H

1200mm³/200mm²=200mm²/200mm²×H

6mm= H

the height is 6mm

c

Volume = length ×width × height

72m³=L×3m ×6m

72m³= L× 18m²

72m³/18m²= L×18m²/18m²

4m =L

the length is 4m

d

Volume = length ×width × height

256cm³=8cm ×w×8cm

256cm³=64cm²×w

256cm³/64cm²=64cm²/64cm²×w

4cm=w

the width is 4cm

e

Volume = length ×width × Height

379.6m³=5.2m×7.3m×H

379.6m³=37.96m²×H

379.6m³/37.96m²=37.96m²/37.96×H

10m=H

the height is 10m

f

Volume = length ×width × Height

288mm³=L×12mm×8mm

288mm³= L×96mm²

288mm³/96mm²= L×96mm²/96mm²

3mm=L

the length is 3mm.

which sign makes the statement true?
A.<
B. >
C. =

Answers

Answer:

-7 1/2 equals to -7.5

so

-7.5 ___ -7.75

-7.5 > -7.75

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