Question

Solve:
$\frac{\cos \theta }{\cos ec\theta +1}+\frac{\cos \theta }{\cos ec\theta -1}=2.$

Answer 1

$\frac{\cos \theta }{cosec\theta +1}+\frac{\cos \theta }{cosec\theta -1}=2$

$\frac{\cos \theta (cosec\theta -1)+\cos \theta (cosec\theta +1)}{cose{c}^2\theta -1}=2$

$\frac{\cos \theta cosec\theta -\cos \theta +\cos \theta cosec\theta +\cos \theta }{{\cot }^2\theta }=2$

$\frac{2\cot \theta }{{\cot }^2\theta }=2$

$2\tan \theta =2$

$\tan \theta =1$

$\theta =\frac{\pi }{4}$.