Question

Prove the following trigonometric identities.

${\displaystyle \cos ec\theta \sqrt{1-{\cos }^2\theta }=1}$

Answer 1

We know that ${\displaystyle {\sin }^2\theta +{\cos }^2\theta =1}$

So,

${\displaystyle \cos ec\theta \sqrt{1-{\cos }^2\theta }=\cos ec\theta \sqrt{{\sin }^2\theta }}$

${\displaystyle =\cos ec\theta \sin \theta }$

${\displaystyle \frac{1}{\sin \theta }\times \sin \theta }$

= 1