Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 497: 67

See below.

$LHS=\frac{sec\theta+tan\theta}{cot\theta+cos\theta}=\frac{sec\theta+tan\theta}{cot\theta+cos\theta}\times\frac{sin\theta cos\theta}{sin\theta cos\theta}=\frac{sin\theta(1+sin\theta)}{cos\theta(cos\theta+sin\theta cos\theta)}=\frac{sin\theta(1+sin\theta)}{cos^2\theta(1+sin\theta)}=\frac{sin\theta}{cos^2\theta}=tan\theta sec\theta=RHS$