Express the given product as a sum or difference only sines

Express the given product as a sum or difference only sines or cosines. cos(11x/2) sin(x/2) cos(11x/2) sin(x/2) = (Simplify your answer.)

Solution

cosAsinB=(1/2)[sin(A+B)-sin(A-B)]

cos(11/2)sin(/2)=(1/2)[sin(11/2 +/2) -sin(11/2 -/2))]

cos(11/2)sin(/2)=(1/2)[sin(12/2) -sin(10/2))]

cos(11/2)sin(/2)=(1/2)[sin(6) -sin(5))]