Question

# If $$\cos^{-1}x+\cos^{-1}y+\cos^{-1}z= 3\pi$$, then value of $$\displaystyle \sum xy$$ equals

A
-3
B
0
C
3
D
-1

Solution

## The correct option is C 3As $$0\le cos^{ -1 }\theta \le \pi$$For $$cos^{ -1 }x+cos^{ -1 }y+cos^{ -1 }z=3\pi$$ this to true$$\Rightarrow cos^{ -1 }x=cos^{ -1 }y=cos^{ -1 }z=\pi \\ \Rightarrow x=y=z=-1\\ \therefore \sum { xy } =xy+yz+zx=(-1)^2+(-1)^2+(-1)^2=3$$Mathematics

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