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

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

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Given that tan 2A = cot (A – 18°)

⇒ cot (90° – 2A) = cot (A – 18°) [∵ tan θ = cot (90 – θ)] 

⇒ 90° – 2A = A – 18° 

⇒ 108° = 3A 

⇒ A =  108° / 3  = 36° 

Hence the value of A is 36°.

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