Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 497: 70

See below.

$LHS=\frac{1-cot^2\theta}{1+cot^2\theta}+2cos^2\theta=\frac{1-cot^2\theta}{1+cot^2\theta}\times\frac{sin^2\theta}{sin^2\theta}+2cos^2\theta=\frac{sin^2\theta-cos^2\theta}{sin^2\theta+cos^2\theta}+2cos^2\theta=sin^2\theta-cos^2\theta+2cos^2\theta=1=RHS$