Question

If \( a = \cos 2\alpha + \sin 2\alpha, b = \cos 2\beta + \sin 2\beta, c = \cos 2\gamma + \sin 2\gamma \) and \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma = 1 \), then \[ \sqrt{abc} = \text{?} \]

• A. \( \sqrt{6} \cos ( \alpha + \beta + \gamma) \)
• B. \( 2 \cos ( \alpha + \beta + \gamma) \)
• C. \( \cos (\alpha + \beta + \gamma) \)
• D. None of these

Hint:

Simplify expressions involving trigonometric identities to solve for unknown values.

Answer 1

The Correct Option is B

By applying trigonometric identities and simplifying, we obtain \( \sqrt{abc} = 2 \cos (\alpha + \beta + \gamma) \).
Step 2: Conclusion.
The correct answer is (B).