A) \[\frac{2\sqrt{6}}{5}\]
B) \[-\frac{2\sqrt{6}}{5}\]
C) \[\frac{1}{5}\]
D) \[-\frac{1}{5}\]
Correct Answer: B
Solution :
\[\cos \,\left( {{\cos }^{-1}}\frac{1}{5}+{{\sin }^{-1}}\frac{1}{5}+{{\cos }^{-1}}\frac{1}{5} \right)=\cos \,\left( \frac{\pi }{2}+{{\cos }^{-1}}\frac{1}{5} \right)\] \[=-\sin \,\left( {{\cos }^{-1}}\frac{1}{5} \right)=-\sin \,\left( {{\sin }^{-1}}\sqrt{\frac{24}{25}} \right)=-\frac{2\sqrt{6}}{5}\].
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