Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to prove

$$\frac{\sin^2(x)}{1+\cos(2x)} = \frac1{2} \tan^2(x)$$

share|cite|improve this question
1  
please do not ask question in imperative mode. – user5501 Apr 20 '11 at 16:38
3  
I have downvoted, so I feel obligated to explain my motives. 1) You have not shown your work, nor indicated that you tried to solve it. 2) Question is asked in imperative mode. 3) Question is ambiguously formatted. 4) By showing no work or interest (except for an answer) at question of this level, I think it is on verge of being too localized. If you address the above points, I would be more than glad to retract my downvote. – user5501 Apr 20 '11 at 16:55
    
Dude please accept an answer. – user9413 Apr 23 '11 at 11:27

Hint: $1+ \cos{2x} = 1 + 2\cos^{2}{x} -1 = 2\cos^{2}{x}$

share|cite|improve this answer

Hint: use the Pythagorean trigonometric identity $\sin^2 x+\cos^2 x=1$ and the double-angle formula $\cos 2x=\cos^2 x-\sin^2 x$

share|cite|improve this answer

Do you know the addition formula $\cos(a+b)=\cos (a)\cos b−\sin (a)\sin (b)$ ? For $a=b=x$ yields $\cos(2x)=\cos^2 (x)−\sin^2 (x)$. Then insert this result into your identity.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.