Question

Prove that: `(sin²A-sin²B)/((sin A cos A)-(sin B cos B))=tan(A+B)`?

Answer 1

`LHS=(sin²A-sin²B)/((sin A cos A)-(sin B cos B))`

`=(2sin(A+B)sin(A-B))/((2sin A cos A)-(2sin B cos B))`

`=(2sin(A+B)sin(A-B))/(sin 2A -sin2 B)`

`=(2sin(A+B)sin(A-B))/(2cos(A+B) sin(A- B))`

`=tan(A+B)=RHS`