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

Question:

What is the value of $\left(1-\cos ^{2} \theta\right) \operatorname{cosec}^{2} \theta ?$

Solution:

We have,

$\left(1-\cos ^{2} \theta\right) \operatorname{cosec}^{2} \theta=\sin ^{2} \theta \times \operatorname{cosec}^{2} \theta$

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

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

$=1$