Help with calc please!! Use a sum-product identity to write sin 5x - sin 3x as a product.

Question

Use a sum-product identity to write sin 5x - sin 3x as a product.

Answer 1

like

sina-sinb=2cos[(a+b)/2]sin[(a-b)/2]

why- let a=x+y, b=x-y

then sina-sinb=sin(x+y)-sin(x-y)=[sinxcosy+cosxsiny]-[sinxxcosy-cosxsiny}

=2cosxsiny

and a+b=x+y+x-y=2x,,,,,, x=(a+b)/2

a-b=2y ,,,,,y=(a-b)/2