Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 33

a. $\tan 4^\circ$ b. $\tan 2\theta$

a. Use the identity $\tan \frac{u}{2}=\frac{\sin u}{1+\cos u}$ with $u=8^\circ$. Then $\frac{\sin 8^\circ}{1+\cos 8^\circ}=\tan \frac{8^\circ}{2}=\tan 4^\circ$. b. Use the identity $\tan \frac{u}{2}=\frac{1-\cos u}{\sin u}$ with $u=4\theta$. Then $\frac{1-\cos 4\theta}{\sin 4\theta}=\tan \frac{4\theta}{2}=\tan 2\theta$.