Question

Simplify 1/1+sin o + 1/1-sin o

Answer 1

Solution

$\frac{1}{1 + sin \: a} + \frac{1}{1 - sin \: a} \\ = \frac{1 - sin \: a + 1 + sin \: a}{(1 - sin \: a)(1 + sin \: a)} \\ = \frac{2}{1 - sin {}^{2} a} \\ = \frac{2}{cos { }^{2}a } \\ = 2sec {}^{2} a$