A) 1
B) 0
C) -3
D) 3
Correct Answer: D
Solution :
Here we have \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi \] and we know that \[0\le {{\cos }^{-1}}x\le \pi \] \[\therefore \] we have \[{{\cos }^{-1}}x=\pi ,\,{{\cos }^{-1}}y=\pi ,\,{{\cos }^{-1}}z=\pi \] \[\therefore \] \[x=y=z=\cos \pi =-1\] \[\therefore \] \[xy+yz+zx=(-1)\,(-1)+(-1)\,(-1)\] \[+\,(-1)\,(-1)\] \[=1+1+1=3\]You need to login to perform this action.
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