If tan2A = cot(A + 18°), where 2A is an acute angle, find the value of A.

Given tan2A = cot(A + 18°)
→ cot(90° - 2A) = cot(A + 18°) [∵ tanθ = cot(90° - θ)]
Comparing angles we get
90° - 2A = A + 18°
→ 90° - 18° = A + 2A
→ 3A = 72°
→ A = 72°/3
→ A = 24°