Question

Show that:
$\frac{1+\cos \theta -{\sin }^2\theta }{\sin \theta (1+\cos \theta )}=\cot \theta .$

Answer 1

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

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

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

$=\cot \theta$.