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

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Question.

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

Solution:

tan2A = cot(A – 18°)

cot (90° – 2A) = cot (A – 18°)

90° – 2A = A – 18°

108° = 3A

A = 36°

If tan 2 A = cot (A – 18°), where 2 A is an acute angle,