An integral

#1
Hi - this is not really statistics, but i thought a kind soul might help anyways.

Its been awhile since i did an integral by hands so I'm a bit rusty. Can someone lead me in the right direction on the integral (2.1) in the attached file?

Thanks.
 

BGM

TS Contributor
#2
For the answer, you can check directly at www.quickmath.com
(or www.calc101.com; if you got an password you can see the steps as well)

But basically you need the product to sum formula,
and use the double angle formula to help:

\( \cos(2x) = 2\cos^2(x) - 1 = 1 - 2\sin^2(x) \)