A) No solution
B) Unique solution
C) Infinite number of solutions
D) None of these
Correct Answer: B
Solution :
We have \[{{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\frac{\sqrt{3}}{2}=\frac{\pi }{6}\] But \[{{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2}\] \ \[{{\sin }^{-1}}x=\frac{\pi }{3}\]and \[{{\cos }^{-1}}x=\frac{\pi }{6}\] Þ \[x=\frac{\sqrt{3}}{2}\]is the unique solution.
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