Question

If \(\sqrt{3} \sin A = \cos A\), then the measure of \(A\) is :

• A. 90°
• B. 60°
• C. 45°
• D. 30°

Hint:

If you see \(\sin\) and \(\cos\) in the same equation with no exponents, aim to create a \(\tan\) or \(\cot\) term to solve it quickly.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To find the angle \(A\), we need to rearrange the equation to use a single trigonometric ratio, typically \(\tan A\), since \(\tan A = \frac{\sin A}{\cos A}\).
Step 2: Key Formula or Approach:
1. Divide both sides by \(\cos A\) to get \(\tan A\).
2. Use the identity \(\tan A = \frac{\sin A}{\cos A}\).
Step 3: Detailed Explanation:
1. Given: \(\sqrt{3} \sin A = \cos A\)
2. Divide both sides by \(\cos A\):
\[ \sqrt{3} \frac{\sin A}{\cos A} = 1 \] 3. Simplify using \(\tan A\):
\[ \sqrt{3} \tan A = 1 \] 4. Isolate \(\tan A\):
\[ \tan A = \frac{1}{\sqrt{3}} \] 5. We know from standard values that \(\tan 30^\circ = \frac{1}{\sqrt{3}}\). Therefore, \(A = 30^\circ\).
Step 4: Final Answer:
The measure of \(A\) is 30°.