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

[kathyjoan]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

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?

 

[kathyjoan]

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?

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?

 

[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? not great

 

[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

 

[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!