Question : Find $\frac{1}{ \sin \theta}-\sin \theta$.
Option 1: $\cos \theta \cot \theta$
Option 2: $\cos \theta \sec \theta$
Option 3: $\cos \theta \operatorname{cosec} \theta$
Option 4: $\cos \theta \tan \theta$
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Correct Answer: $\cos \theta \cot \theta$
Solution :
Given:
$\frac{1}{ \sin \theta}-\sin \theta$
$= \frac{1-\sin^2\theta}{\sin\theta}$
$= \frac{\cos^2\theta}{\sin\theta}$
$= \cot\theta \cos\theta$
Hence, the correct answer is $\cot\theta \cos\theta$.
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