Question:
If $\tan \theta=\frac{8}{15}$ then $\operatorname{cosec} \theta=?$
(a) $\frac{15}{17}$
(b) $\frac{17}{15}$
(c) $\frac{17}{8}$
(d) $\frac{8}{17}$
Solution:
Given : $\tan \theta=\frac{8}{15}$
Since, $\tan \theta=\frac{P}{B}$
$\Rightarrow P=8$ and $B=15$
Using Pythagoras theorem,
$P^{2}+B^{2}=H^{2}$
$\Rightarrow 8^{2}+(15)^{2}=H^{2}$
$\Rightarrow H^{2}=64+225$
$\Rightarrow H^{2}=289$
$\Rightarrow H=17$
Therefore,
$\operatorname{cosec} \theta=\frac{H}{P}=\frac{17}{8}$
Hence, the correct option is (c).
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