To do the power reducing formula, we're going to think of this as two sine squared X quantity squared. Well, we don't want exponents, so we want to think about what else could sine squared X be thought of as? And sine squared X is really the same thing as one minus cosine 2X over two. And we're going to quantity square that. So we get two. We're going to foil out the top, so we get 1 -, 2 cosine 2X plus cosine squared 2X all over 4. From there, the two and the four we could pull out and have it be as a half. The 1 -, 2 cosine 2X is OK, but now this cosine squared, we can't have a cosine squared 2X so we're going to have this turn into one plus cosine of 4X all over two. So now we could distribute so we can combine like terms in a moment. So when we distribute or we get 1 + 1/2 or three halves and three halves times a half would give us 3/4 and then half times -2 is just going to give us a -1 cosine 2X and 1/2 * 1/2 on the cosine 4X is going to give us 1/4 cosine 4X. Now if you don't remember this formula, remember that cosine of 2X was just two cosine squared X -, 1. So if we add a one and then we divide by two, we can see that cosine squared X is really just one plus cosine 2X over 2. And we know that cosine squared cosine of 2X is also 1 -, 2 sine squared X. So now if I take 2 sine squared X on one side, 1 minus cosine 2X on the other, divide by two, we can see that sine squared X is really just one minus cosine 2X over 2. So those are the two formulas that I used here. I took out sine squared X and I put in what sine squared X equaled, IE this piece right here. Then after doing the algebra, I then took this cosine squared 2X and put in what the cosine squared equaled, which was that one plus cosine 2X over 2. And at this point we have to double the angle. So the fact that the angle here started out as a 2X meant that we want twice as much, or we want 4X.