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Question

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


A
-3
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B
0
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C
3
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D
-1
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Solution

The correct option is C 3
As $$0\le cos^{ -1 }\theta \le \pi $$
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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