How do you verify the identity sectheta/sintheta-sintheta/costheta=cottheta?

Aug 23, 2016

Please see the Proof in Explanation.

Explanation:

$\text{The L.H.S.}$=sectheta/sintheta - sintheta/costheta#

$= \frac{\frac{1}{\cos} \theta}{\sin} \theta - \sin \frac{\theta}{\cos} \theta$

$= \frac{1}{\sin \theta \cos \theta} - \sin \frac{\theta}{\cos} \theta$

$= \frac{1 - {\sin}^{2} \theta}{\sin \theta \cos \theta}$

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

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

$= \cot \theta$

$= \text{The R.H.S.}$

Hence, the Proof.

Enjoy Maths.!