Question

Verify the ID:
sin(x+y)-sin(x-y)=2cosxsiny

Answer 1

Rearrange the left side using:

sin(x+y)=sinxcosy+cosxsiny

and

sin(x-y)=sinxcosy-cosxsiny

Some stuff will cancel out after this and then you should see how to rearrange it to 2cosxsiny

Answer 2

These are known as some of the sum and difference formulas