Hello,

We know that the cosine is the real part of

So by some changes,

We then have :

Which is, by the identity you're given, equal to :

Now, since you want to take the real part of this fraction, transform the denominator into a real number : multiply the numerator and the denominator by the complex conjugate of , which is

By using the identity , we get in the denominator :

And in the numerator, using basic algebraic operations and rearranging, we get :

Since we only want the real part, we may only keep the first line.

And then the red part is exactly

So finally, we have :

By the half angle formula, we have

And by the identity (because the sine function is odd)

So

And we can simplify... :

Note : Some steps have been left to your understanding...