How do you verify sin(x+y)/cos(x)cos(y)=tan(x)+tan(y)

Question

I want to know how to verify this problem

Answer 1

Expand sin(x + y) using an identity.

 

sin(x + y) / [cos(x)cos(y)] = [sin(x)cos(y) + cos(x)sin(y)] / [cos(x)cos(y)] 

 

= sin(x)/cos(x) + sin(y)/cos(y) = tan(x) + tan(y)