# How do you verify the identify costhetacscthetatantheta=1?

Aug 2, 2016

#### Explanation:

All trigonometric ratios can be easily expressed in terms of $\sin \theta$ and $\cos \theta$.

For example, $\tan \theta = \sin \frac{\theta}{\cos} \theta$, $\cot \theta = \cos \frac{\theta}{\sin} \theta$, $\sec \theta = \frac{1}{\cos} \theta$ and $\csc \theta = \frac{1}{\sin} \theta$

Hence, $\cos \theta \csc \theta \tan \theta$

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

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

= $1$