A) 0
B) 1
C) \[\frac{4}{5}\]
D) \[\frac{1}{5}\]
Correct Answer: D
Solution :
[d] Let \[\sin \left[ {{\sin }^{-1}}\left( \frac{1}{5} \right)+{{\cos }^{-1}}x \right]=1\] \[\Rightarrow {{\sin }^{-1}}\left( \frac{1}{5} \right)+{{\cos }^{-1}}x={{\sin }^{-1}}1\] \[\Rightarrow {{\sin }^{-1}}\left( \frac{1}{5} \right)+{{\cos }^{-1}}x=\frac{\pi }{2}\] \[\Rightarrow {{\cos }^{-1}}x=\frac{\pi }{2}-{{\sin }^{-1}}\left( \frac{1}{5} \right)={{\cos }^{-1}}\left( \frac{1}{5} \right)\] \[\Rightarrow x=\frac{1}{5}\]
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