# How do you verify the identify cotthetasectheta=csctheta?

Aug 2, 2016

The following identities are very important:

$\tan \alpha = \sin \frac{\alpha}{\cos} \alpha$

$\csc \alpha = \frac{1}{\sin} \alpha$

$\sec \alpha = \frac{1}{\cos} \alpha$

$\cot \alpha = \frac{1}{\tan} \alpha$

Applying the aforementioned identities:

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

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

$\frac{\cancel{\cos \theta}}{\sin} \theta \times \frac{1}{\cancel{\cos \theta}} = \frac{1}{\sin} \theta$

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

Identity proved!!

Hopefully this helps!