A) \[\pi -{{\sin }^{-1}}\left( \frac{63}{65} \right)\]
B) \[\pi -{{\cos }^{-1}}\left( \frac{33}{65} \right)\]
C) \[\frac{\pi }{2}-{{\sin }^{-1}}\left( \frac{56}{65} \right)\]
D) \[\frac{\pi }{2}-{{\cos }^{-1}}\left( \frac{9}{65} \right)\]
Correct Answer: C
Solution :
\[{{\sin }^{-1}}\left( \frac{12}{13} \right)-{{\sin }^{-1}}\left( \frac{3}{5} \right)\] \[{{\sin }^{-1}}\left( x\sqrt{1-{{y}^{2}}}-y\sqrt{1-{{x}^{2}}} \right)\] \[={{\sin }^{-1}}\left( \frac{33}{65} \right)={{\cos }^{-1}}\left( \frac{56}{65} \right)=\frac{\pi }{2}-{{\sin }^{1}}\left( \frac{56}{65} \right)\]
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