If tan2A = cot(A – 18°) where 2A is an acute angle. Find the value of A.

Given that, 2A is an acute angle.

⇒ 2A < 90°

So, using trigonometric identity, we can say that

cot (90° - 2A) = tan 2A [∵, cot (90° - θ) = tan θ]

Now, replace tan 2A by cot (90° - 2A) in the given question.

tan 2A = cot (A – 18°)

⇒ cot (90° - 2A) = cot (A – 18°)

Now, we can compare the degrees from above, we get

90° - 2A = A – 18°

⇒ 2A + A = 90° + 18°

⇒ 3A = 108°

⇒ A = 108°/3

⇒ A = 36°

Thus, the value of A is 36°.