Chapter 5 - Section 5.4 - Product-to-Sum and Sum-to-Product Formulas - Exercise Set - Page 689: 24

Please see below.

We verify as below: $$\frac{\sin 3x + \sin x }{\cos 3x + \cos x}= \frac{2\sin \frac{3x+x}{2}\cos \frac{3x-x}{2}}{\cos \frac{3x+x}{2} \cos \frac{3x-x}{2}} \\ =\frac{\sin 2x \cos x }{\cos 2x \cos x}=\tan 2x$$