Question

What is the value of (1 − cos² θ) cosec² θ? 

Answer 1

We have, 

${\displaystyle (1-{\cos }^2\theta )\cos e{c}^2\theta ={\sin }^2\theta \times \cos e{c}^2\theta }$

=${\displaystyle {\sin }^2\theta \times {\left(\frac{1}{\sin \theta }\right)}^2}$ 

= ${\displaystyle {\sin }^2\theta \times \frac{1}{{\sin }^2\theta }}$ 

${\displaystyle =1}$