I need this to be worked out step by step asap

Try using the identities for sin(2x) and cos(2x).

sin(2x) = 2 sinxcosx
cos(2x) = cos^2x - sin^2x = 1 - 2sin^2x = 2 cos^2x -1

One of these identities for cos(2x) makes your proof come right out.