Multiple choice

(\text{If } \tan 2A = \cot (A - 21^\circ), \text{ where } 2A \text{ is an acute angle, then find the value of } A.)

  1. $\(39^\circ\)$
  2. $\(47^\circ\)$
  3. $\(43^\circ\)$
  4. $\(37^\circ\)$

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since tan(2A) = cot(A - 21°) and cot θ = tan(90° - θ), we have tan(2A) = tan(90° - (A - 21°)) = tan(111° - A). Therefore 2A = 111° - A, giving 3A = 111° and A = 37°. We verify 2A = 74° is acute, satisfying the condition. Options A, B, C result from algebraic errors in solving the equation.

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