If tan 2A = cot (A — 12°), where 2A is an acute angle, find the value of A.
We are given that: tan 2A = cot (A – 12°)
∴We can rewrite it as: cot (90° - 2A) = cot (A – 12°)
On comparing both sides, we get,
90° - 2A = A – 12 °
⇒ A + 2A = 90° + 12°
⇒ 3A = 102°
⇒ A = 34°