Question:
What is the value of $9 \cot ^{2} \theta-9 \operatorname{cosec}^{2} \theta ?$
Solution:
We have,
$9 \cot ^{2} \theta-9 \operatorname{cosec}^{2} \theta=9\left(\cot ^{2} \theta-\operatorname{cosec}^{2} \theta\right)$
$=-9\left(\operatorname{cosec}^{2} \theta-\cot ^{2} \theta\right)$
We know that, $\operatorname{cosec}^{2} \theta-\cot ^{2} \theta=1$
Therefore, $9 \cot ^{2} \theta-9 \operatorname{cosec}^{2} \theta=-9$
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