Question
What is the value of $9\cot^2\theta-9\text{ cosec}^2\theta?$
✓
Answer
We have,
$9\cot^2\theta-9\text{cosec}^2\theta$
$=9(\cot^2\theta-\text{cosec}^2\theta)$
$=-9(\text{cosec}^2\theta-\cot^2\theta)$
We know that, $\text{cosec}^2\theta-\cot^2\theta=1$
Therefore, $9\cot^2\theta-9\text{cosec}^2\theta=-9$
$9\cot^2\theta-9\text{cosec}^2\theta$
$=9(\cot^2\theta-\text{cosec}^2\theta)$
$=-9(\text{cosec}^2\theta-\cot^2\theta)$
We know that, $\text{cosec}^2\theta-\cot^2\theta=1$
Therefore, $9\cot^2\theta-9\text{cosec}^2\theta=-9$
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