Verify the identity cosx ycosx cosy Verify the identity sin

Verify the identity: cos(x + y)/cosx cosy Verify the identity: sin^2x - sin^2y = sin(x + y)sin(x - y)

1) cos(x+y)/cosxcosy = 1 - tanxtany

LHS : cos(x+y)/cosxcosy

= [cosxcosy -sinxsiny ]/cosxcosy

= 1- sinxsiny/cosxcosy

= 1 - (sinx/cosx)(siny/cosy)

= 1 - tanxtany

RHS

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

RHS sin(x+y)sin(x-y)

= [ sinxcosy +cosxsiny][ sinxcosy - cosxsiny]

= sin^2xcos^2y - sinxcosycosxsiny +cosxsinxsinycosy - cos^2xsin^2y

=sin^2xcos^2y - cos^2xsin^2y

= sin^2x - sin^2y