A) \[1\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[0\]
D) \[\frac{\sqrt{3}}{2}\]
E) \[-1\]
Correct Answer: A
Solution :
Given, \[{{\cos }^{-1}}\left( \frac{5}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x\] \[\Rightarrow \]\[{{\sin }^{-1}}\left( \frac{12}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x\] \[\Rightarrow \] \[{{\cos }^{-1}}x=0\Rightarrow \cos 0\] \[\Rightarrow \] \[x=1\]
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