Question
What is the value of $(1+\cot^2\theta)\sin^2\theta?$
✓
Answer
We have,
$(1+\cot^2\theta)\sin^2\theta=\text{cosec}^2\theta\times\sin^2\theta$
$=\Big(\frac{1}{\sin\theta}\Big)^2\times\sin^2\theta$
$=\frac{1}{\sin^2\theta}\times\sin^2\theta$
$=1$
$(1+\cot^2\theta)\sin^2\theta=\text{cosec}^2\theta\times\sin^2\theta$
$=\Big(\frac{1}{\sin\theta}\Big)^2\times\sin^2\theta$
$=\frac{1}{\sin^2\theta}\times\sin^2\theta$
$=1$
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