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  • If cos inverse alpha plus cos inverse beta plus cos inverse gamma equal to 3 pi then alpha into bracket beta plus gamma plus beta into bracket gamma plus alpha plus gamma into bracket alpha plus beta equals A.0 B.1 C.6 D.12

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

Answers (1)

Answer :(C)

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

Posted by

infoexpert24

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