Please answer the following two problems and show work Expre

Please answer the following two problems and show work.

Express the given product as a sum or difference containing only sines or cosines. sin (8x) cos (3x) sin (8x) cos (3x) Simplify your answer.)

sin(8x) cos (3x)

This is of the form sin A cos B which is equal to (1/2)(sin(A+B)+sin(A-B))

so we get

(1/2)(sin(8x+3x)+sin(8x-3x))

which is equal to

(1/2)(sin (11x)+sin(5x))

sin 3x -sin x

This is of the form sin A -sin B which is equal to 2cos((A+B)/2)sin((A-B)/2

so we get

2cos((3x+x)/2)sin(3x-x)/2)

2cos 2x sin x