Question

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

Answer 1

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