How to Prove sin4x/1-cos4x * (1-cos2x/cos2x) = tanx

[Vee9]

Homework Statement

How would you prove:

sin4x/ 1-cos4x * (1-cos2x/cos2x) = tanx

It was our Thinking and Inquiry question on our test today and I didn't know how to prove it.

The Attempt at a Solution

I'm not sure if I was headed in the right direction but this is what I did:
LS:
2(2sinxcosx)/ 1-2(1-2sin^x) * (1-(1-2sin^2x)) / cos 2x
And then I expanded from there.
What I tried to do was to change everything to that it was SIN on top and COS on bottom to get TAN, but I didn't know how to continue.

 

[vela]

You didn't apply the trig identities correctly. For example,

sin 4x = sin 2(2x) = 2 sin 2x cos 2x

You had sin 4x = 4 sin x cos x, which isn't correct. Try to get everything in terms of cos 2x and sin 2x first. Simplify that as much as you can and then turn everything into plain old sin x and cos x.

 

[tiny-tim]

Welcome to PF!

Hi Vee9! Welcome to PF!

(try using the X² icon just above the Reply box )

Much simpler is to use the equation sin2x/(1 - cos2x) = … ?

 

[Vee9]

Hi Vee9! Welcome to PF!

(try using the X² icon just above the Reply box )

Much simpler is to use the equation sin2x/(1 - cos2x) = … ?

What will happen to the "4's" in the first part?

 

[tiny-tim]

What will happen to the "4's" in the first part?

uhh?

it's a general formula!

get on with it! ​