If $\tan \theta=\frac{8}{15}$ then $\operatorname{cosec} \theta=?$
(a) $\frac{17}{8}$
(b) $\frac{8}{17}$
(c) $\frac{15}{17}$
(d) $\frac{17}{15}$
$\tan \theta=\frac{8}{15}$
$\Rightarrow \frac{1}{\tan \theta}=\frac{15}{8}$
$\Rightarrow \cot \theta=\frac{15}{8} \quad \ldots \ldots(1)$
Now,
$\operatorname{cosec}^{2} \theta=1+\cot ^{2} \theta$
$\Rightarrow \operatorname{cosec}^{2} \theta=1+\left(\frac{15}{8}\right)^{2} \quad$ [Using (1)]
$\Rightarrow \operatorname{cosec}^{2} \theta=1+\frac{225}{64}=\frac{289}{64}$
$\Rightarrow \operatorname{cosec} \theta=\sqrt{\frac{289}{64}}=\frac{17}{8}$
Hence, the correct answer is option (a).
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.