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If \( \cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi \), then \( \alpha(\beta+\gamma) + \beta(\gamma+\alpha) + \gamma(\alpha+\beta) \) is equal to:

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For inverse trigonometric sums: Always recall principal value ranges. If sum equals maximum possible value, each term must be maximal. \( \cos^{-1}x = \pi \Rightarrow x = -1 \)

Updated On: Mar 2, 2026

\( 0 \)
\( 1 \)
\( 6 \)
\( 12 \)

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The Correct Option is C

Solution and Explanation

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If \( \cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi \), then \( \alpha(\beta+\gamma) + \beta(\gamma+\alpha) + \gamma(\alpha+\beta) \) is equal to:

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The Correct Option is C

Solution and Explanation

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