I needd helppp. I can't verify this identity! Pleasee help and show full work. Thanks :)

Ok, you need to find some way to break down the 'cubes' in the cos and sin functions.

Separate the cos^3 and sin^3 into cos(x)cos^2(x) and sin(x)sin^2(x) respectively:



Use the identity cos^2(x) + sin^2(x) = 1:



Expand;



Rearrange;



Factor out cos(x)sin(x) from the two last terms in the numerator;



Factor out sin(x) + cos(x) from the numerator in all the terms together;



It's done now. :) Only one little step more.

If I may show another way.

Note the sum of two cubes in the numerator. Factoring it, gives:



The sin(x)+cos(x) cancels and we are left with:



Note the identity

This leaves us with