A) No solution
B) Only one solution
C) Two solutions
D) Three solutions
Correct Answer: A
Solution :
Given equation is \[2{{\cos }^{-1}}x+{{\sin }^{-1}}x=\frac{11\pi }{6}\] Þ \[{{\cos }^{-1}}x+({{\cos }^{-1}}x+{{\sin }^{-1}}x)=\frac{11\pi }{6}\] Þ \[{{\cos }^{-1}}x+\frac{\pi }{2}=\frac{11\pi }{6}\] \[\Rightarrow {{\cos }^{-1}}x=4\pi /3\] which is not possible as \[{{\cos }^{-1}}x\in [0,\,\pi ]\].
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