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: Understand the given equation:
We are given the equation \( \tan A = 3 \cot A \), and we need to find the measure of angle \( A \).

Step 2: Use the identity for \( \cot A \):
We know that \( \cot A = \frac{1}{\tan A} \). Substituting this into the given equation, we get:
\[ \tan A = 3 \times \frac{1}{\tan A} \] Multiply both sides of the equation by \( \tan A \) (assuming \( \tan A \neq 0 \)):
\[ \tan^2 A = 3 \]

Step 3: Solve for \( \tan A \):
Taking the square root of both sides:
\[ \tan A = \sqrt{3} \quad \text{or} \quad \tan A = -\sqrt{3} \] Since \( \tan A = \sqrt{3} \) corresponds to the angle \( A = 60^\circ \), we select this solution (assuming the principal value for \( A \) is between \( 0^\circ \) and \( 180^\circ \)).

Step 4: Conclusion:
The measure of angle \( A \) is \( \boxed{60^\circ} \).