Okay, I'm trying to simplify a trigonometric thing. I say "thing" because it's not an equation, and that has me a little confused.

Beginning:

So, I'm not given what that is equal to, but told to factor and simplify. I looked up the answer, and they gave me the last two steps.

Second-to-last:

Last:

Okay, getting from the second-to-last step to the last is easy, using the double-angle formulae. I just don't know how to get from the beginning to the second-to-last step! I checked it out in MS Excel, and

does in fact equal

... I just don't know how they got there. Is it that there is some common factor in the first two terms of the original thing? Can I divide each side of a subtraction operation in half or something?