If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A[CBSE 2009]

Given: tan 2A = cot(A - 18)

by complementary angle formula

cot(90 - A) = tan A

From the question,

tan 2 A = cot (90 - 2A)

Therefore,

cot(90 - 2A) = cot(A - 18)

Now both the angles will be equal, so

90° – 2A = A – 18°

108° – 2A = A

3A = 108°

A = 108/3 = 36°

A = 36°