A) \[-1\]
B) \[\frac{2}{5}\]
C) \[\frac{1}{3}\]
D) \[1\]
E) \[\frac{1}{5}\]
Correct Answer: E
Solution :
\[\sin \left( {{\sin }^{-1}}\left( \frac{1}{5} \right)+{{\cos }^{-1}}x \right)=1\] \[\Rightarrow \] \[{{\sin }^{-1}}\left( \frac{1}{5} \right)+{{\cos }^{-1}}x=\frac{\pi }{2}\] \[\Rightarrow \] \[{{\sin }^{-1}}\left( \frac{1}{5} \right)=\frac{\pi }{2}-{{\cos }^{-1}}x\] \[\Rightarrow \] \[{{\sin }^{-1}}\left( \frac{1}{5} \right)={{\sin }^{-1}}x\] \[\Rightarrow \] \[x=\frac{1}{5}\]
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