Integration of even powers of sine and cosine

[lydia_y620]

Homework Statement

Homework Equations

cos²x = (1+cos2x)/2
sin²x = (1-cos2x)/2

The Attempt at a Solution

I believe you would use the double angle formula repeatedly but that is very tedious; is there a more concise way to solve the problem?

 

[PeroK]

What about using $cos^2x + sin^2x =1$?

 

[lydia_y620]

What about using $cos^2x + sin^2x =1$?

okay, I've figured it out. Thanks!