Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 498: 63

See below.

$RHS=\frac{1-sin^2(\frac{\theta}{2})/cos^(\frac{\theta}{2})}{1+sin^2(\frac{\theta}{2})/cos^(\frac{\theta}{2})}=\frac{cos^2(\frac{\theta}{2})-sin^2(\frac{\theta}{2})}{cos^2(\frac{\theta}{2})+sin^2(\frac{\theta}{2})}=\frac{cos\theta}{1}=cos\theta=LHS$