A) \[\frac{2\sqrt{6}}{5}\]
B) \[\frac{-2\sqrt{6}}{5}\]
C) \[\frac{1}{5}\]
D) \[\frac{-1}{5}\]
Correct Answer: B
Solution :
Key Idea: \[{{\cos }^{-1}}x+{{\sin }^{-1}}x=\frac{\pi }{2},\,\,\forall x\in R\] \[\cos \left[ 2{{\cos }^{-1}}\frac{1}{5}+{{\sin }^{-1}}\frac{1}{5} \right]\] \[=\cos \left[ {{\cos }^{-1}}\frac{1}{5}+{{\sin }^{-1}}+\frac{1}{5}+{{\cos }^{-1}}\frac{1}{5} \right]\] \[=\cos \left( \frac{\pi }{2}+{{\cos }^{-1}}\frac{1}{5} \right)\] \[=-\sin \left( {{\cos }^{-1}}\frac{1}{5} \right)\] \[=-\sin \left( {{\sin }^{-1}}\sqrt{\frac{24}{25}} \right)\] \[=-\sqrt{\frac{24}{25}}=\frac{-2\sqrt{6}}{5}\]
You need to login to perform this action.
You will be redirected in
3 sec
