Question

If \( 2 \cos 3\theta = 1 \), then the value of \( \theta \) will be:

• A. \( 10^\circ \)
• B. \( 15^\circ \)
• C. \( 20^\circ \)
• D. \( 25^\circ \)

Hint:

When solving trigonometric equations, use known values for standard angles such as \( \cos 60^\circ = \frac{1}{2} \).

Answer 1

The Correct Option is B

Step 1: Solve the equation.
We are given the equation \( 2 \cos 3\theta = 1 \). To solve for \( \theta \), first divide both sides by 2: \[ \cos 3\theta = \frac{1}{2} \]
Step 2: Use the known value of \( \cos \theta \).
We know that \( \cos 60^\circ = \frac{1}{2} \). So: \[ 3\theta = 60^\circ \]
Step 3: Solve for \( \theta \).
Now, divide both sides by 3: \[ \theta = \frac{60^\circ}{3} = 20^\circ \]
Step 4: Conclusion.
Thus, the value of \( \theta \) is \( 20^\circ \). Therefore, the correct answer is (C).