If sec 5A = cosec (A – 36°) and 5A is an acute angle, show that A = 21°.

Question

Philoid · Accepted Answer

We are given that: sec 5A = cosec (A – 36°)

∴We can rewrite it as: cosec (90° – 5A) = cosec (A – 36°)

On comparing both sides, we get,

90° – 5A = A – 36°

⇒ A + 5A = 90° + 36°

⇒ 6A = 126°

⇒ A = 21°

Hence, proved.