Question : The value of $\left(\operatorname{cosec}^2 B-1\right)\left(\sec ^2 B-1\right)$ is:
Option 1: 4
Option 2: 3
Option 3: 2
Option 4: 1
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Correct Answer: 1
Solution : Given: $\left(\operatorname{cosec}^2 B-1\right)\left(\sec ^2 B-1\right)$ We know that $\operatorname{cosec}^2 B = 1 + \cot^2 B$ $\sec^2 B = 1 + \tan^2 B$ $\left(\operatorname{cosec}^2 B-1\right)\left(\sec ^2 B-1\right) = \cot^2 B\times\tan^2 B$. $=\cot^2 B \times \tan^2 B = \frac{1}{\tan^2 B}\times\tan^2 B = 1$ Hence, the correct answer is 1.
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