Question:
What is the value of $\left(1-\cos ^{2} \theta\right) \operatorname{cosec}^{2} \theta ?$
Solution:
We have,
$\left(1-\cos ^{2} \theta\right) \operatorname{cosec}^{2} \theta=\sin ^{2} \theta \times \operatorname{cosec}^{2} \theta$
$=\sin ^{2} \theta \times\left(\frac{1}{\sin \theta}\right)^{2}$
$=\sin ^{2} \theta \times \frac{1}{\sin ^{2} \theta}$
$=1$