Verify the identity tan x + cot x / tan x - cot x = 1/ sin^2x - cos^2x

Answers

Answer 1

Answer:

$(\tan x+\cot x)/(\tan x-\cot x)=(1)/(\sin^2x-\cos^2x)\n\n\text{use}\ \tan x=(\sin x)/(\cos x),\ \cot x=(\cos x)/(\sin x)\n\n\tan x+\cot x=(\sin x)/(\cos x)+(\cos x)/(\sin x)=(\sin x\cdot\sin x)/(\sin x\cos x)+(\cos x\cdot\cos x)/(\sin x\cos x)\n\n=(\sin^2x+\cos^2x)/(\sin x\cos x)\n\n\text{use}\ \sin^2x+\cos^2x=1\n\n=(1)/(\sin x\cos x)\n\n\tan x-\cot x=(\sin x)/(\cos x)-(\cos x)/(\sin x)=(\sin^2x-\cos^2x)/(\sin x\cos x)$

$L_s=(\tan x+\cot x)/(\tan x-\cot x)=((1)/(\sin x\cos x))/((\sin^2x-\cos^2x)/(\sin x\cos x))=(1)/(\sin x\cos x)\cdot(\sin x\cos x)/(\sin^2x-\cos^2x)\n\n=(1)/(\sin^2x-\cos^2x)=R_s\n\nL_s=R_s\Rightarrow The\ identity.$

Related Questions

4) At the end of the summer, I decide to drain the swimming pool. I noticed that it drains faster when there is more water in the pool. That was interesting to me, so I decided to measure rate at which it drains. I found that it was draining at a rate of 3% every 5 minutes How many gallons are left in the pool after 50 minutes?
Is 102 divisible by 4 5 6 9 or 10 PLEASE HELP I AM FAILING AND ABOUT TO CRY!!!!
Ben is greeting customers at a music store. Of the first 20 people he sees enter the store, 9 are wearing jackets and 11 are not. What is the experimental probability that the next person to enter the store will be wearing a jacket? Enter your answer as a simplified fraction.
Estimate how many 12 inch rulers will be about the same length as a the object flag
I need help evaluating this problem

50 POINTS WILL MARK BRAINIEST PLEASE HELP ME!! THANK YOU

Answers

a)The more hours spent on homework resulted in higher test scores, seen by the positive correlation between x and y values.
b) It predicts, for 3 hours, a 64.
c) It means that even if the student did absolutely no homework at all, he'd still make at least a 40 on the test.

Answer:

A. There is a strong positive correlation.

B. The regression line predicts 64%. The graph suggests 60%.

C. When the hours of homework completed is 0, the baseline test score is 40%

True or false: any nonzero integers, the product and the quotient have the same sign. Why?

Answers

False. This is because no matter what the number is, the properties of multiplication and division stay the same. So, if one odd and even number multiply/divide, then the answer will be negative. But, if two numbers of the same sign (both either negative or positive) are divided/multiplied, they will both be positive. Therefore, the result is not always the same sign as the starting integers

Hope this helped! :D

Please help fast! I'll mark brainliest rate 5 and thank if you get it right/answer FAST Georgia has at most $100 to spend at the outlet mall. She wants to buy a swimsuit for $60 and spend the rest on earrings. Each pair of earrings cost $10.75.
Which inequality can be used to determine the maximum number of pairs of earrings Georgia can buy?
A. 60 – 10.75x≤ 100
B. 60 + 10.75x≤ 100
C. 60 – 10.75x≥ 100
D. 60 + 10.75x≥ 100

Answers

total cost is less than or equal to 100 sice cant spend more than have
cost<100
cost=swim+earings
costearings=xearints imes 10.75
swim=60

60+10.75x<100

B

Answer:

Step-by-step explanation:

What are the cofficients in the expression 8y2 +12x-5y+7

Answers

the coefficients are 8,12 and 5

What is 2/3 times 4/5 in fraction form

Answers

We have that for the Question "what is 2/3 times 4/5 in fraction form" it can be said that We have that what 2/3 times 4/5 in fraction form is

$x=(8)/(15)$

From the question we are told

what is 2/3 times 4/5 in fraction form

Generally the equation for the Multiplication is mathematically given as

$x=(2)/(3)*(4)/(5)\n\n$

$x=(8)/(15)$

Therefore

We have that what 2/3 times 4/5 in fraction form is

$x=(8)/(15)$ \

For more information on this visit

brainly.com/question/19007362

(2/3)* (4/5)
= (2*4) / (3*5)
= 8/15

The final answer is 8/15~

How do you do square feet of outdoor carpet with holes in it?

Answers

Find the length and width of the carpet, and multiply the two numbers together. Depending on the size of the holes, you can just round the square footage to what you came up with before. If the holes are significantly sized, measure from one side of the hole to the other to find the holes diameter. Divide the diameter in half to find the radius, and square it. (To square it is multiplying it by itself.) Multiply the radius squared by 3.14. Repeat this on every hole, and subtract it from the square footage of the blanket if it didn't have the holes.

Other Questions

Evaluate the expression when a = –1.4 and b = –2.7. |a| + b A.–1.3 B.–4.1 C.4.1 D.1.3Solve for x. A.x = 35 B. 9 2/7 C.x = 63 D. 31 1/2 Graph the solution of the inequality. 14 < 2t + 18 ≤ 20

The expression 3 1/2x + 18 represents the perimeter of the rectangle shown. Write an expression that represents the length of the rectangle.

The area of a rectangular photograph is 35 square inches. If the width of the photo is 5 inches, how tall is the photo.

Daily temperatures for two cities, Salem and Oxford, were recorded for one week. A 8-column table has 2 rows. Column 1 has entries Salem, Oxford. Column 2 is labeled Sunday with entries 56, 71. Column 3 is labeled Monday with entries 61, 52. Column 4 is labeled Tuesday with entries 55, 58. Column 5 is labeled Wednesday with entries 62, 50. Column 6 is labeled Thursday with entries 58, 89. Column 7 is labeled Friday with entries 61, 60. Column 8 is labeled Saturday with entries 61, 61. Using statistics, answer the question below: Which city had the highest variability in temperatures?