prove sinxcosy = (1/2)(sin(x+y)+sin(x-y))

Question

sinxcosy = (1/2)(sin(x+y)+sin(x-y))

left side is the given

Answer 1

sinxcosy=(1/2)(sin[x+y]+sin[x-y])

break up sinxcosy into halves

(1/2)sinxcosy+(1/2)sinxcosy=

add and subtract (1/2)cosxsiny

(1/2)sinxcosy+(1/2)sinxcosy+(1/2)cosxsiny-(1/2)cosxsiny=

group terms

[(1/2)sinxcosy+(1/2)cosxsiny]+[(1/2)sinxcosy-(1/2)cosxsiny)]=

(1/2)sin(x+y)+(1/2)sin(x-y)=

(1/2)[sin(x+y)+sin(x-y)]