Sin(a-b)sin(a+b)+sin^2b

Question

Sin(a-b)sin(a+b)+sin^2b

Answer 1

sin(a-b)sin(a+b)+sin²b=½(cos(a-b-a-b)-cos(a-b+a+b))+sin²b=½(cos(-2b)-cos(2a))+½(1-cos(2a))=½cos(-2b)=½cos(2b)