How does one prove sin(x+y) - sin(x-y) = 2cos(x) sin(y)?

1 Answer
Apr 16, 2018

In description

Explanation:

sin (x+y)-sin (x-y)sin(x+y)sin(xy)
=sinxcosy+sinycosx-(sinxcosy-sinycosx)=sinxcosy+sinycosx(sinxcosysinycosx)
=sinxcosy+sinycosx-sinxcosy+sinycosx=sinxcosy+sinycosxsinxcosy+sinycosx
=cancel (sinxcosy)+sinycosx-cancel (sinxcosy)+sinycosx
=sinycosx+sinycosx
=2sinycosx henceforth proved.