Verify the identity: sin(x+y)+sin(x-y)=2sinxcosy

Question

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

Answer 1

Use the addition/subtraction angle identity for sine to work out the left side.  The left side should match the right side.

 

sin(x + y) = sinxcosy + cosxsiny

sin(x - y) = sinxcosy - cosxsiny

 

If we add them together, we get 2sinxcosy, which is the right side of the identity.