Question

Prove that sin(x+y)/sin(x-y)=tan(x+y)/tan(x-y)

Answer 1

Tan x +tany=sinxcosx+sinycosy

=sinxcosy+coaxing

=sin (x+y)cosx.cosy #

Similarly tanx-tany=sin (x-y)cost. Cosy $

From # and $ we get

Tanx+tany/ tanx-tany=sin (x-y)