Question

Evaluate $\frac{\sin 54^{\circ}}{\cos 36^{\circ}}+\frac{\sec 46^{\circ}}{\operatorname{cosec} 44^{\circ}}$

• A. 0
• B. -1
• C. 2
• D. 1

Answer 1

Answer:

C. 2

Solution:

Formula used:

sin ( 90 - θ ) = cosθθ , sec ( 90 - θ ) = cosecθ 

Calculation:

sin 54^∘/cos 36^∘ + sec 46^∘/cosec 44^∘ 

As, we know that sin( 90 - θ ) = cosθ  , sec (90 - θ ) = cosecθ 

⇒ sin ( 90 - 36 ) /cos36 + sec( 90 - 44 ) /cosec44

⇒ cos36/cos36 + cosec44/cosec44 = 1 + 1 = 2  

Hence, the required value is 2 .