Question

When evaluating the integral Sin^m xCos^n xdx, which formula or law is most useful if the powers of both sin and cosine are even?

Answer 1

If I remember correctly:
\[sin^2x+cos^2x=1\]
You can solve for either and substitute, but it's been a few since I did those problems and I hated trig based integrals ;)

Answer 2

Hmm, looked it up. My bad. It's the half angle identities.

Answer 3

\[sin^2x=\frac{1-cos(2x)}{2}\]
and
\[cos^2x=\frac{1+cos(2x)}{2}\]

Answer 4

The first answer I listed is for use in odd problems.

Answer 5

i think they also call it reducing powers?

Answer 6

Half Angle Formula got it!