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: Understanding the given equation:
We are given the equation \( \tan A = 3 \cot A \), and we need to find the value of angle \( A \).
We know that \( \cot A = \frac{1}{\tan A} \).

Step 2: Substituting the cotangent expression:
Substitute \( \cot A = \frac{1}{\tan A} \) into the equation: \[ \tan A = 3 \times \frac{1}{\tan A} \] This simplifies to: \[ \tan^2 A = 3 \]

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

Step 4: Finding the angle A:
For \( \tan A = \sqrt{3} \), the value of \( A \) is: \[ A = 60^\circ \quad \text{(since \( \tan 60^\circ = \sqrt{3} \))} \] For \( \tan A = -\sqrt{3} \), the value of \( A \) is: \[ A = 120^\circ \quad \text{(since \( \tan 120^\circ = -\sqrt{3} \))} \]

Step 5: Conclusion:
The measure of angle \( A \) is either \( 60^\circ \) or \( 120^\circ \).