Show that 2sinxcosy=sin(x+y)+sin(x-y)- Please, check my work

2sinxcosy=sin(x+y)+sin(x-y)

=sin(x+y)+sin(x-y)

=sinxcosy+cosxsiny+ (sinxcosy- cosxsiny)

=sinxcosy+cosxsiny+ sinxcosy- cosxsiny

=sinxcosy+ sinxcosy

= 2sinxcosy

Thank You.

Looks fine to me!

once in a blue moon

sin (x + y) = sin x cos y + cos x sin y
sin (x - y) = sin x cos y - cos x sin y

Sum = 2 sin x cos y