Question

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

Answer 1

$\frac{\sin \theta }{1+\cos \theta }+\frac{1+\cos \theta }{\sin \theta }=\frac{{\sin }^2\theta +1+2\cos \theta +{\cos }^2\theta }{(1+\cos \theta )\sin \theta }$

$=\frac{2+2\cos \theta }{(1+\cos \theta )\sin \theta }=\frac{2(1+\cos \theta )}{(1+\cos \theta )\sin \theta }=2co\sec \theta$