Question

Prove the following trigonometric identities.

(i) $\cot \theta -\tan \theta =\frac{2{\cos }^2\theta -1}{\sin \theta \cos \theta }$
(ii) $\tan \theta -\cot \theta =\frac{2{\sin }^2\theta -1}{\sin \theta \cos \theta }$

Answer 1

(i) We have to prove

We know that,

So,

(ii) We have to prove

We know that,

So,