Question

If $\tan \mathrm{\theta }=\frac{8}{15}\mathrm{then}\mathrm{cosec}\mathrm{\theta }=?$
(a) $\frac{15}{17}$

(b) $\frac{17}{15}$

(c) $\frac{17}{8}$

(d) $\frac{8}{17}$

Answer 1

$$\begin{gathered} \mathrm{Given}:\tan \theta =\frac{8}{15} \\ \mathrm{Since},\tan \theta =\frac{P}{B} \\ \Rightarrow P=8\mathrm{and}B=15 \\ \mathrm{Using}\mathrm{Pythagoras}\mathrm{theorem}, \\ {P}^2+B^2=H^2 \\ \Rightarrow 8^2+{\left(15\right)}^2=H^2 \\ \Rightarrow H^2=64+225 \\ \Rightarrow H^2=289 \\ \Rightarrow H=17 \\ \mathrm{Therefore}, \\ \mathrm{cosec}\theta =\frac{H}{P}=\frac{17}{8} \end{gathered}$$

Hence, the correct option is (c).