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