Question

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

Answer 1

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

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

$=\cos \theta \left(\frac{\frac{2}{\sin \theta }}{\frac{{\cos }^2\theta }{{\sin }^2\theta }}\right)$

$=2\times \frac{sin\theta }{cos\theta }$

$=2\tan \theta$

$=RHS$

Hence proved