Question
If $\sin\theta=\frac{1}{3},$ then find is the value of $2\cot^2\theta+2$.
✓
Answer
$\sin\theta=\frac{1}{3}$
$\therefore\ \text{cosec }\theta=\frac{1}{\sin\theta}=\frac{3}{1}$
Now, $2\cot^2\theta+2=2(\cot^2\theta+1)$
$=2\text{cosec}^2\theta=2\times(3)^2$
$=2\times9=18$
$\therefore\ \text{cosec }\theta=\frac{1}{\sin\theta}=\frac{3}{1}$
Now, $2\cot^2\theta+2=2(\cot^2\theta+1)$
$=2\text{cosec}^2\theta=2\times(3)^2$
$=2\times9=18$
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