Question

PLEASE HELP Trig Idenities

Answer 1

$\dfrac{\sin(A+B)}{\sin(A-B)}=\dfrac{\sin A\cos B+\cos A\sin B}{\sin A\cos B-\cos A\sin B}$

Divide through all terms by $\cos A\cos B$. Then, for instance, the first term in the numerator becomes

$\dfrac{\sin A\cos B}{\cos A\cos B}=\dfrac{\sin A}{\cos A}=\tan A$

All other terms reduce similarly, giving the final product

$\dfrac{\tan A+\tan B}{\tan A-\tan B}$