2 Attachment(s)

Stuck finding area under the curve

I'm stuck at the question 51 in my textbook.

I can find the two equations and know the f(x)=y=1 is greater than g(x). I follow the solutions and get stuck at the part where they go from 1 - cos^2 x = sin^2 x.

1 - cos^2 x makes sense to me since it's f(x) - g(x) but where does the sin^2 x come from. And from this point on I don't understand why they divide it by 2 and create the integral off the interval.

One attachment has the textbook question, #51 and the other is my solutions book scan.