If tan 2A = cot(A - 30°) and 2A is an acute angle, then find 'A' is-

Question: If tan 2A = cot(A - 30°) and 2A is an acute angle, then find 'A' is-

Solution:
Given that,
tan 2A = cot (A - 30°)
⇒ tan 2A = tan [90° - (A - 30°)]
⇒ 2A = 90° - A + 30°
⇒ 3A = 120°
⇒ A = 120°/3
∴ A = 40°