Solve this

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).

 

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