Answer is below
See explanation below.
We will begin the proof from the right-hand side of the identity.
First, let's expand the parentheses:
Then, let's apply the standard trigonometric identities
Let's factorise the numerator of the fraction using the "middle-term break":
One of the Pythagorean identities is
We can rearrange it to get:
Let's apply this rearranged identity to our proof:
Let's factorise the denominator, which is in the form of a difference of two squares: