Inverse Trigonometric Functions Question 241
Question: If $ {{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi , $ then $ xy+yz+zx= $
[Karnataka CET 2003]
Options:
A) 0
B) 1
C) 3
D) -3
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ {{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi $
$ \because 0\le {{\cos }^{-1}}x\le \pi $
$ \therefore 0\le {{\cos }^{-1}}y\le \pi $ and $ 0\le {{\cos }^{-1}}z\le \pi $ Here $ {{\cos }^{-1}}x={{\cos }^{-1}}y={{\cos }^{-1}}z=\pi $
$ \Rightarrow x=y=z=\cos \pi =-1 $ \ $ xy+yz+zx $
$ =(-1)(-1)+(-1)(-1)+(-1)(-1) $
$ =1+1+1=3 $ .
BETA
