Greetings. You don't need any other trig identities. Everything is on the diagram

Step 1. Fill in the angles, and you'll see that the 3rd from left triangle and the large triangle are similar.

Step 2. Find the scale factor.

In this case, the large triangle has a hypotenuse of 1 and the small triangle has a hypotenuse of

Hence scale factor(Q):

Step 3. Apply this to the other side of the triangle, opposite the angle of .

Hence:

Put into

And you get:

Simplify, then look at your triangle and realize that

Substitute and you arrive at the formula