A) 0
B) \[\frac{1}{\sqrt{5}}\]
C) \[\frac{2}{\sqrt{5}}\]
D) \[\frac{\sqrt{3}}{2}\]
Correct Answer: B
Solution :
\[\because \] \[{{\cot }^{-1}}\frac{1}{2}={{\cos }^{-1}}\frac{1}{\sqrt{5}}\] Hence given equation can be written as \[{{\sin }^{-1}}x+{{\cos }^{-1}}\frac{1}{\sqrt{5}}=\frac{\pi }{2}\] \[\Rightarrow \]\[x=\frac{1}{\sqrt{5}}\].
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