Question
What is the value of $(1-\cos^2\theta)\text{ cosec}^2\theta?$
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Answer
$(1-\cos^2\theta)\text{cosec}^2\theta=\sin^2\theta\times\text{cosec}^2\theta$
$\begin{Bmatrix}\because1-\cos^2\theta=\sin^2\theta\text{ and }\sin\theta\text{ cosec }\theta=1\end{Bmatrix}$
$=(\sin\theta\text{ cosec }\theta)^2$
$=(1)^2=1$
$\begin{Bmatrix}\because1-\cos^2\theta=\sin^2\theta\text{ and }\sin\theta\text{ cosec }\theta=1\end{Bmatrix}$
$=(\sin\theta\text{ cosec }\theta)^2$
$=(1)^2=1$
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