If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.
Correct: A
We use the complementary angle identity: tan θ = cot (90° - θ). So, we can write tan 2A as cot (90° - 2A). The given equation becomes cot (90° - 2A) = cot (A - 18°). Equating the angles (since cot function is one-to-one for acute angles): 90° - 2A = A - 18°. Collect terms with A on one side and constants on the other: 90° + 18° = A + 2A. 108° = 3A. A = 108° / 3 = 36°.