Question

$\frac{\sec 32°}{\mathrm{cosec}58°}=?$

(a) $\frac{2}{3}$

(b) $\frac{16}{29}$

(c) $\frac{16}{3}$

(d) 1

Answer 1

$$\begin{gathered} \frac{\sec 32°}{\mathrm{cosec}58°}=\frac{\sec \left(90°-58°\right)}{\mathrm{cosec}58°} \\ =\frac{\mathrm{cosec}58°}{\mathrm{cosec}58°}\left(\because \sec \left(90°-\theta \right)=\mathrm{cosec}\theta \right) \\ =1 \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{d}\right). \end{gathered}$$