Question

Question #b0676

Answer 1

LHS
`=sin(x+y)sin(x-y)`
`=(sinxcosy+cosxsiny)*(sinxcosy-cosxsiny)`
`=(sin^2xcos^2y-cos^2xsin^2y)`
`=(sin^2x(1-sin^2y)-(1-sin^2x)sin^2y)`
`=(sin^2x-cancel(sin^2x*sin^2y)-sin^2y+cancel(sin^2xsin^2y))`
`=(sin^2x-sin^2y)`=RHS