Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 30

a. $\tan 14^\circ$ b. $\tan 14\theta$

a. Use the formula $\tan 2x=\frac{2\tan x}{1-\tan^2x}$ with $x=7^\circ$. Then $\frac{2\tan 7^\circ}{1-\tan^2 7^\circ}=\tan (2*7^\circ)=\tan 14^\circ$. b. Use the formula $\tan 2x=\frac{2\tan x}{1-\tan^2x}$ with $x=7\theta$. Then $\frac{2\tan 7\theta}{1-\tan^2 7\theta}=\tan (2*7\theta)=\tan 14\theta$.