Question

If tan A = 3 cot A, then the measure of the angle A is :

• A. 15°
• B. 30°
• C. 45°
• D. 60°

Answer 1

The Correct Option is D

Step 1: Equation Analysis
Given equation: \( \tan A = 3 \cot A \). Objective: Determine angle \( A \).
Key identity: \( \cot A = \frac{1}{\tan A} \).

Step 2: Substitution and Simplification
Substitute \( \cot A = \frac{1}{\tan A} \) into the given equation:\[\tan A = 3 \times \frac{1}{\tan A}\]This simplifies to:\[\tan^2 A = 3\]

Step 3: Solving for \( \tan A \)
Taking the square root of both sides yields:\[\tan A = \pm \sqrt{3}\]Therefore, \( \tan A = \sqrt{3} \) or \( \tan A = -\sqrt{3} \).

Step 4: Determining Angle \( A \)
If \( \tan A = \sqrt{3} \), then \( A \) is:\[A = 60^\circ \quad (\text{because } \tan 60^\circ = \sqrt{3})\]If \( \tan A = -\sqrt{3} \), then \( A \) is:\[A = 120^\circ \quad (\text{because } \tan 120^\circ = -\sqrt{3})\]

Step 5: Final Result
Angle \( A \) is either \( 60^\circ \) or \( 120^\circ \).