Question

Prove that $\frac{\cos \theta }{1-\sin \theta }+\frac{\cos \theta }{1+\sin \theta }=4$.

Answer 1

Given, $\frac{\cos \theta }{1-\sin \theta }+\frac{\cos \theta }{1+\sin \theta }=4$

$\Rightarrow \cos \theta \left[\frac{1+\sin \theta +1-\sin \theta }{1-{\sin }^2\theta }\right]=4$

$\Rightarrow \cos \theta \frac{2}{{\cos }^2\theta }=4$

$\Rightarrow \cos \theta =\frac{1}{2}$

$\Rightarrow \theta =2n\pi +\frac{\pi }{3},2n\pi +\left(5\frac{\pi }{3}\right)$