Question

Simplify the trigonometric expression.

Answer 1

https://study.ashworthcollege.edu/access/content/group/3deb3864-16e6-41b5-8cfd-6102f85fcfab/algebra2_exam_14_files/mc001-1.jpg

Answer 2

get common denominators to add those two fractions:
\(\large \frac{1}{1+sin\theta}+\frac{1}{1-sin\theta} \)

=\(\large \frac{1}{1+sin\theta}\color {red}{\cdot \frac{1-sin\theta}{1-sin\theta}}+\frac{1}{1-sin\theta}\color {red}{\cdot \frac{1+sin\theta}{1+sin\theta}} \)

=\(\large \frac{1-sin\theta}{1-sin^2\theta}+\frac{1+sin\theta}{1-sin^2\theta} \)

=\(\large \frac{1-sin\theta +1+sin\theta}{1-sin^2\theta} \)

=\(\large \frac{2}{1-sin^2\theta}=\frac{2}{cos^2\theta}=2sec^2\theta \)