Question

# If $$\displaystyle \cos \:^{-1}x+\cos \:^{-1}y+\cos ^{-1}z=3\pi$$ then the value of $$xy+yz+zx$$ is

A
3
B
1
C
3
D
none of these

Solution

## The correct option is C $$3$$If  $$y=cos^{-1}(x)$$   $$R\epsilon[\pi,0]$$ where$$R$$ is the range of $$y$$.Therefore in the above case, which is only possible if$$cos^{-1}(x)=cos^{-1}(y)=cos^{-1}(z)=\pi$$Hence$$x=y=z=-1$$Therefore $$xy+yz+zx$$$$=3 (-1)^2=3$$Mathematics

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