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

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

We have 
tan 2A = cot (A- 18°)
⇒ cot (90° - 2A) = cot (A -18°)
Equating angles,
⇒ 90° - 2A = A- 18° ⇒ 108° = 3A
⇒ A = 36°

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