Question:medium
If \( \cos^{-1} \alpha + \cos^{-1} \beta + \cos^{-1} \gamma = 3\pi \), then the value of \( \alpha(\beta+\gamma) + \beta(\gamma+\alpha) + \gamma(\alpha+\beta) \) is:
If \( \cos^{-1} \alpha + \cos^{-1} \beta + \cos^{-1} \gamma = 3\pi \), then the value of \( \alpha(\beta+\gamma) + \beta(\gamma+\alpha) + \gamma(\alpha+\beta) \) is:
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When dealing with inverse trigonometric equations involving sums of inverse cosines, check if each term attains boundary values like \( 0 \) or \( \pi \) for easy simplification.
Updated On: Nov 28, 2025
- \( 0 \)
- \( 1 \)
- \( 6 \)
- \( 12 \)
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