Question

Prove the equation:-
$\sqrt{\frac{1+cos\theta }{1-cos\theta }}=cosec\theta +cot\theta$

Answer 1

Given :

$\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}=\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}\times \sqrt{\frac{1+\cos \theta }{1+\cos \theta }}=\frac{1+\cos \theta }{\sqrt{1-{\cos }^2\theta }}=\frac{1+\cos \theta }{\sin \theta }=\csc \theta +\cot \theta$

Hence proved