Q. 355.0( 1 Vote )

# If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β (γ + α) + γ (α + β) equalsA. 0B. 1C. 6D. 12

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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