Question

Prove that:

$\tan \theta -\cot \theta =2\cot 2\theta$

Answer 1

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

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

$=\frac{2\left[\cos 2\theta \right]}{\sin 2\theta }$

$=2\cot 2\theta$