how do I solve... cos 2x - cos4x = tan3x tanx(cos2x + cos4x)?
I need to prove that is an identity, I do not need to find the value for x

Question

debbieg · Answer

is it this:$$\cos(2x)-\cos(4x)=\tan(3x)\tan x[\cos(2x)+\cos(4x)]$$
are you solving for x?

anonymous · Answer

yes he is

anonymous · Answer

I need to prove that is an identity,

anonymous · Answer

aha

debbieg · Answer

OK, that's what I thought... "solve" implies something else so threw me off. This looks like a doozy, I'll take a look at it.

anonymous · Answer

first of all, keep the tan3x tanx terms on right hand side and remaining cos terms to one side,
then break the tan3x tanx into (sin3x sinx)/ (cos3x cosx) then apply|dw:1377047409549:dw|

anonymous · Answer

Those identities are off by a factor of two I think...

anonymous · Answer

|dw:1377047648403:dw|

anonymous · Answer

@SandeepReddy The identities should be
$$
\sin A\sin B = \frac{1}{2}\left[ \cos(A-b) - \cos(A+B) \right]
$$and so on. (Obviously the halves just cancel, but that doesn't make the identities right!)

But great trick!

debbieg · Answer

Slick, @SandeepReddy  :)

debbieg · Answer

Oops, yes good point @Erin001001 ! I see what you mean.

anonymous · Answer

@Erin001001  you are right at that half part, i almost forgot to include it, thanx for that :)