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
\[
\sqrt{abc} = \text{?}
\]
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
\[
\sqrt{abc} = \text{?}
\]
Show Hint
Simplify expressions involving trigonometric identities to solve for unknown values.
Updated On: Jan 12, 2026
- \( \sqrt{6} \cos ( \alpha + \beta + \gamma) \)
- \( 2 \cos ( \alpha + \beta + \gamma) \)
- \( \cos (\alpha + \beta + \gamma) \)
- None of these
Show Solution
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The Correct Option is B
Solution and Explanation
By applying trigonometric identities and simplifying, we obtain \( \sqrt{abc} = 2 \cos (\alpha + \beta + \gamma) \).
Step 2: Conclusion.
The correct answer is (B).
Step 2: Conclusion.
The correct answer is (B).
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