Question

Show that $\cot \theta -\tan \theta =2\cot 2\theta$.

Answer 1

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