Help with a proof

1. Nov 21, 2007

kathyjoan

1. The problem statement, all variables and given/known data

sin4x/(1-cos4x) * (1-cos2x)/cos2x = tan x

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 21, 2007

HallsofIvy

Staff Emeritus
Well, gosh, there seems to be some things missing! Do you really think saying "I don't feel like making any attempt at all" is a good way to convince people to help you?

3. Nov 21, 2007

kathyjoan

I have tried sin4x=sin(2x+2x)=2sin2xcos2x

(2sin2x/(1-cos4x))*1-cos2x

(2sin2x-2sin2xcos2x)/(1-cos4x)

2sin2x(1-cos2X)/1-cos4x

cos2x=1-2sin^2x

cos4x= cos^2 2x + sin^2 2x

can I do sin2x=sin(x+x)=sinxcosx+cosxsinx=sinx(2cosx)

I end up with 4sinxcosx=tanx?

4. Nov 21, 2007

kathyjoan

5. Nov 21, 2007

rock.freak667

Let me start you off on an easier path
$$\frac{sin4x}{1-cos4x} * \frac{1-cos2x}{cos2x}$$

remember that $sin4x=2sin2xcos2x$, you replace sin4x by that identity...will anything there cancel out and make the expression simpler to prove?

EDIT:2sin2x(1-cos2X)/1-cos4x

you're nearly there actually...remember $cos2A=1-2sin^2A$ if A=2x then you'll have an identity for cos4x...use it and you'll get it out

6. Nov 21, 2007

kathyjoan

Okay

I am left with 2sin2x(1-cos2x)/-2sin^2 2x
wow! okay then cos 2x=1-2sin^2x
2sin^2x/-sin2X
2sin^2x/-2sinxcosx=sin/cos wha la Thanks so very much!!!