Question

Evaluate the following and justify your answer.

sec 16° cosec 74° – cot 74° tan 16°.

Answer 1

Given sec 16° cosec 74° – cot 74° tan 16°

= sec 16° . cosec (90° – 16°) – cot (90° – 16°) . tan 16° 

= sec 16°. sec 16° – tan 16° . tan 16° 

[∵ cosec (90° – θ) = sec θ; cot (90° – θ) — tan θ] 

= sec² 16° – tan² 16° 

= 1 [∵ sec² θ – tan² θ = 1]