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

Solution :

Given,   tan 2A = cot(A – 18)

\(\implies\)  cot(90 – 2A) = cot(A – 18)

\(\implies\)  90 – 2A = A – 18

\(\implies\)  3A = 108

\(\implies\)  A = 36