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