Question : Evaluate $\frac{\sin 54^{\circ}}{\cos 36^{\circ}}+\frac{\sec 46^{\circ}}{\operatorname{cosec} 44^{\circ}}$
Option 1: 0
Option 2: –1
Option 3: 2
Option 4: 1
Correct Answer: 2
Solution :
Given: $\frac{\sin 54^{\circ}}{\cos 36^{\circ}}+\frac{\sec 46^{\circ}}{\operatorname{cosec} 44^{\circ}}$
= $\frac{\sin 54^{\circ}}{\cos (90^{\circ}-54^{\circ})}+\frac{\sec 46^{\circ}}{\operatorname{cosec} (90^{\circ}-46^{\circ})}$
= $\frac{\sin 54^{\circ}}{\sin 54^{\circ}}+\frac{\sec 46^{\circ}}{\sec 46^{\circ}}$
= $1 + 1$
= $2$
Hence, the correct answer is 2.
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