Perform indicated operation and simplify the results so that

Perform indicated operation and simplify the results so that there are no quotients.

Thank you for your help!

Solution

(sin alpha - cos alpha)^2

(a-b)^2=a^2 +b^2-2ab

(sin alpha - cos alpha)^2= sin^2 alpha + cos^2 alpha - 2sin alpha cos alpha

        and sin^2 theta + cos^2theta=1 and 2sin theta cos theta=sin 2 theta

So we get

(sin alpha - cos alpha)^2= 1- sin 2alpha