1. The problem statement, all variables and given/known data This question comes from calculating the Einstein A and B coefficients. I am supposed to find the average value of cos(x)^2 over the solid angle of a sphere which is 1/3. And I need to show this. A similar course in a different uni just says that For unpolarized, isotropic radiation, the expectation of cos(x)^2=1/3 2. Relevant equations cos(2x)=2cos(x)^2-1 3. The attempt at a solution I tried using the average integral equation however i always end up with 1/2. I've tried 1/pi *∫cos(X)^2dx and just use the trig equation that I have given. However the answer comes out as 1/2 and I do not know how to get 1/3. I also tried integrating from 0 to 2pi etc. Thankful for any help!