really hard trig problem?

Question

i don't understand this...at all. work please.

(3 sin X + cos 3X) / (cos X - sin X) = 1 + 2 sin 2X

i'm supposed to solve/prove the identity?

Answer 1

Use identities such as
Sin(A+B) = SinACosB + CosASinB
(of course, Sin(2X) is the same as Sin(X+X) so it is simply a case where A=B=X.

Cos(A+B) = CosACosB - SinASinB
(first step, use A=2X and B=X
This will leave you with some Sin2X and Cos2X which you can then resolve using the identity again
(Cos(2X) = Cos(X+X)