Question:
$\frac{\sec 32^{\circ}}{\operatorname{cosec} 58^{\circ}}=?$
(a) $\frac{2}{3}$
(b) $\frac{16}{29}$
(c) $\frac{16}{3}$
(d) 1
Solution:
$\frac{\sec 32^{\circ}}{\operatorname{cosec} 58^{\circ}}=\frac{\sec \left(90^{\circ}-58^{\circ}\right)}{\operatorname{cosec} 58^{\circ}}$
$=\frac{\operatorname{cosec} 58^{\circ}}{\operatorname{cosec} 58^{\circ}} \quad\left(\because \sec \left(90^{\circ}-\theta\right)=\operatorname{cosec} \theta\right)$
$=1$
Hence, the correct option is (d).