Question : The value of $(\frac{1}{\sin\theta}+\frac{1}{\tan\theta})(\frac{1}{\sin\theta}-\frac{1}{\tan\theta})$ is:
Option 1: 0
Option 2: 2
Option 3: 3
Option 4: 1
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Correct Answer: 1
Solution :
Given:
$(\frac{1}{\sin\theta}+\frac{1}{\tan\theta})(\frac{1}{\sin\theta}-\frac{1}{\tan\theta})$
$= (\operatorname{cosec}\theta+\cot\theta)(\operatorname{cosec}\theta-\cot\theta)$
$=\operatorname{cosec}^2\theta-\cot^2\theta$
$= 1$
Hence, the correct answer is 1.
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