Q. 355.0( 1 Vote )

If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β (γ + α) + γ (α + β) equals
A. 0

B. 1

C. 6

D. 12

Answer :

Given, cos–1α + cos–1β + cos–1γ = 3π … (1)


Principal value of cos-1 x is [0, π]


So, maximum value which cos-1 x can have is π.


So, if (1) is correct then all the three terms i.e,


cos–1α, cos–1β, cos–1γ should be equal to π


So, cos–1α = π


cos–1β = π


cos–1γ = π


So, α = β = γ = -1


So, α(β + γ) + β (γ + α) + γ (α + β)


= (-1)(-1-1) + (-1)(-1-1) + (-1)(-1-1)


= 3(-1)(-2)


= 6

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