Question:
The value of $\frac{\tan ^{2} \theta-\sec ^{2} \theta}{\cot ^{2} \theta-\operatorname{cosec}^{2} \theta}$ is
(a) –1
(b) $\frac{1}{2}$
(c) $\frac{-1}{2}$
(d) 1
Solution:
$\frac{\tan ^{2} \theta-\sec ^{2} \theta}{\cot ^{2} \theta-\operatorname{cosec}^{2} \theta}$
$=\frac{-1}{-1} \quad\left(1+\tan ^{2} \theta=\sec ^{2} \theta\right.$ and $\left.1+\cot ^{2} \theta=\operatorname{cosec}^{2} \theta\right)$
$=1$
Hence, the correct answer is option (d).
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