# What is the value of (1 + cot2 θ) sin2 θ?

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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