Question

Prove that:

$\cot \theta -\cot 2\theta =cosec2\theta$.

Answer 1

Now,

$\cot \theta -\cot 2\theta$

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

$=\frac{\sin 2\theta .\cos \theta -\cos 2\theta .\sin \theta }{\sin \theta .\sin 2\theta }$

$=\frac{\sin (2\theta -\theta )}{\sin \theta .\sin 2\theta }$

$=\frac{1}{\sin 2\theta }$

$=\csc 2\theta$.