Question

Prove the following:
$\frac{\sin 5x+\sin 3x}{\cos 5x+\cos 3x}=\tan 4x$

Answer 1

$LHS=\frac{\sin 5x+\sin 3x}{\cos 5x+\cos 3x}=\frac{2\sin \left(\frac{5x+3x}{2}\right)\cos \left(\frac{5x-3x}{2}\right)}{2\cos \left(\frac{5x+3x}{2}\right)\cos \left(\frac{5x-3x}{2}\right)}$

$=\tan 4x=RHS$

Hence proved.