Question : Find the value of $\cot ^2B- \operatorname{cosec}^2B$ for $ 0<B<90^{\circ}.$
Option 1: $1$
Option 2: $2$
Option 3: $–1$
Option 4: $–2$
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Correct Answer: $–1$
Solution :
Given: $\cot^2 B-\operatorname{cosec}^2 B$
$=\frac{\cos^{2} B}{\sin ^{2} B}- \frac{1}{\sin^{2} B}$
$= \frac{\cos^{2}-1}{\sin ^{2} B}$
$= \frac{-\sin ^{2} B}{\sin ^{2} B}$
$=-1$
Hence, the correct answer is $-1$.
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