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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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tan 2A = cot(A – 18°) 

= cot[90 – [90 – (A – 18°)]] 

tan 2A = tan [90 – (A – 18°)] 

2A = 90-(A – 18°) = 90 – A + 18° 

⇒ 3A = 108° 

∴ A = 36°

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