Question

How can i prove: cos x/sin^2 x-cos x cot^2 x = cot x sin x

Answer 1

sin2x=.....

Answer 2

Sorry i ment sin^2(x)

Answer 3

Then cot 2x=.....

Answer 4

:/

Answer 5

\[\frac{cos x}{sin^2 x-cos x} cot^2 x = cot x sin x\] Is this the question?

Answer 6

The minus cos x is not under the division bar

Answer 7

k
\[\frac{cosx}{sin^2x}−cosxcot^2x=cotxsinx\]
Correct?

Answer 8

Yes.

Answer 9

ok @AravindG it's yours, and can you help me, I'm out of patience and ideas? http://openstudy.com/study#/updates/532bb32ce4b01b0501029215

Answer 10

@Lizz111 Did you try taking LCM?

Answer 11

Im not sure how to do that.

Answer 12

(Make the left side into one big fraction) ie. 1/3 +1/4=(1+1)/12

Answer 13

(a/b)+(c/d)=(ad+bc)/bd

Answer 14

Develop the left side. Replace cot^2x by (cos^2 x)/(sin^2 x)
cos x/sin^2 x - [cos x*(cos^2 x)]/sin ^2 x =
= [cos x(1 - cos^2 x)]/sin^2 x = (cos x*sin^2 x)/sin^2 x = cos x
The question might be wrong?

Answer 15

I dont believe the question is wrong, but im not sure.

After i find the LCM, what do i do from there?

Answer 16

first, write out your steps. Even the teeniest tiniest

Answer 17

I haven't actually done it yet, but we can see if it's right or wrong

Answer 18

Develop the right side: cot x*sin x = (cos x/sin x)*sin x = cos x
Both the left and right side are equal to cos x, then the equation is proven.

Answer 19

Can you explain this step. Where did the (1- cos^2 x) come from. I know its equal to sin^2 x.

cos x/sin^2 x - [cos x*(cos^2 x)]/sin ^2 x = [cos x(1 - cos^2 x)]/sin^2 x

Answer 20

You remember \(sin^2x+cos^x=1\)?

Answer 21

Yes.

Answer 22

so that's how we do the sub, but first we have to set it up. We have: \[\frac{cos x - cos x*(cos^2 x)}{sin ^2 x} = \frac{[cos x(1 - cos^2 x)]}{sin^2 x}\] Do you see?

Answer 23

I sorta understand. I guess my algebra skills are failing me and not my precalc. But i dont understand what is allowing you to sub that in?

Answer 24

oh, just that they are equal. That's it just like we can sub secx for 1/cosx

Answer 25

so we pulled out a cosx from each term, then we happened to have something useful

Answer 26

Wait so did you multiply the cos x and the cos ^2 x together then factor out the cos x?

Answer 27

yea, sort of

Answer 28

So you got cos x - cos^3 x then factored out the cos x ?

Answer 29

yea

Answer 30

Okay. I understand. Thank you very much! I really appreciate it!

Answer 31

np, so if you want, can you step by step, justifying as you go, tell me the proof?