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Class 12 Inverse Trigonometric Functions · Mcq Single Correct1 Marksinverse_trigonometric_identities

Class 12 Maths · Inverse Trigonometric Functions · Mcq Single Correct #15

If \(\cos^{-1}\alpha+\cos^{-1}\beta+\cos^{-1}\gamma=3\pi\), find \(\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)\).

(A) 0
(B) 1
(C) 6
(D) 12

✅ Step-by-Step Solution

Final Answer: Option (C): 6

Each principal arccosine is at most π. Their sum reaches 3π only if all equal π, hence α=β=γ=−1. Each of the three displayed products is 2, giving 6.

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