A) No solution
B) Unique solution
C) Infinite solution
D) None of these
Correct Answer: B
Solution :
[b] \[{{\sin }^{-1}}x-co{{s}^{-1}}x=co{{s}^{\text{-}1}}\left( \frac{\sqrt{3}}{2} \right)\] \[\Rightarrow \frac{\pi }{2}-co{{s}^{-1}}x-co{{s}^{\text{-}1}}x={{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] \[\Rightarrow \frac{\pi }{2}-\frac{\pi }{6}=2co{{s}^{\text{-}1}}x\] \[\Rightarrow \frac{\pi }{3}=2co{{s}^{\text{-}1}}x\] \[\Rightarrow co{{s}^{\text{-}1}}x=\frac{\pi }{6}\] \[\Rightarrow x=\frac{\sqrt{3}}{2}\] i.e. unique solution
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