Chapter 7 - Analytic Trigonometry - 7.4 Trigonometric Identities - 7.4 Assess Your Understanding - Page 475: 10

b

$\frac{1}{1-sin(\theta)}+\frac{1}{1+sin(\theta)}=\frac{(1+sin(\theta))+(1-sin(\theta))}{(1+sin(\theta)(1-sin(\theta)}=\frac{2}{1-sin^2(\theta)}$. The identity says: $sin^2(\theta)+cos^2(\theta)=1$. Hence $\frac{2}{1-sin^2(\theta)}=\frac{2}{cos^2(\theta)}=2sec^2(\theta)$. Hence the answer is b.