Why does the trig expression just disappear?

[adamaero]

Homework Statement

Homework Equations

3. Solution

Then the equations from part (A) are used--but why does the converted trig (1-cos(etc)) go away?
Does this have to do with the mean-squared bit?

 

[kuruman]

It becomes 1 when you time-average over one period.$$\frac{\int_0^{2\pi}(1-\cos x)dx}{\int_0^{2\pi}dx}=1$$