Math
posted by Chiquesta on .
Express sin^6theta in multiples of costheta and hence evaluate the integral of sin^6theta from 0 to pi/2.
Thanks in advance! :)

sin^6θ = (sin^2θ)^3
= (1  cos^2θ)^3
= 1  3cos^2θ + 3cos^4θ + cos^6θ
Now you can use your halfangle formula
cos^2θ = (1 + cos 2θ)/2
to get no exponents and multiples of θ.
You will end up with
1/192 (60θ  45sin2θ + 9sin4θ  sin6θ)
from 0 to pi/2 yields 30pi/192