If $cos^{-1}\alpha + cos^{-1}\beta +cos^{-1}\gamma = 3\pi , $ then $\alpha ( \beta + \gamma ) + \beta (\gamma +\alpha ) + \gamma ( \alpha + \beta )$ equals :
Answer & explanation
Correct answer: option 3
The correct answer is option (3) → 6
$\cos^{-1}\alpha + \cos^{-1}\beta +\cos^{-1}\gamma = 3\pi$
⇒ iff $α=β=γ=-1$
so $α(β+γ)+β(γ+α)+γ(α+β)$
$=2+2+2=6$