A) \[\frac{12}{13}\]
B) \[-\frac{12}{13}\]
C) \[\frac{5}{12}\]
D) None of these
Correct Answer: A
Solution :
Let \[{{\sin }^{-1}}\frac{5}{13}=x\,\,\Rightarrow \,\,\sin x=\frac{5}{13}\] \[\Rightarrow \,\,\cos x=\sqrt{1-\frac{25}{169}}=\frac{12}{13}\] \[\Rightarrow \,\,\cos \,\left( {{\sin }^{-1}}\frac{5}{13} \right)=\cos \,\,\left( {{\cos }^{-1}}\frac{12}{13} \right)=\frac{12}{13}\].
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