Multiple choice

If $\tan 2A = \cot (A - 21^{\circ})$, where $2A$ is an acute angle, then $\angle A =$ ____

  1. $24^{\circ}$
  2. $27^{\circ}$
  3. $35^{\circ}$
  4. $37^{\circ}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the identity tan(theta) = cot(90 - theta), we have tan(2A) = cot(90 - 2A). Thus, 90 - 2A = A - 21. Solving for A: 3A = 111, so A = 37 degrees.

AI explanation

Using the cofunction identity, if tan 2A equals cot(90 minus 2A), we can set the angles equal: 90 minus 2A equals A minus 21. Solving this linear equation gives 3A equals 111, which means A is 37 degrees.

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