Question

determine whether the equation is an identity

Answer 1

it isn't. this is done by manipulating it until you get a very simple equation that clearly contradicts ittself.

only re-arrange the left side, changing cos^4(x) to cos^2(x)(1 - sin^2(x)) and sin^4(x) to sin^2(x)(1 - cos^2(x)), you'll see :)