A) \[\frac{65}{56}\]
B) \[\frac{24}{65}\]
C) \[\frac{16}{65}\]
D) \[\frac{56}{65}\]
Correct Answer: D
Solution :
Given \[{{\sin }^{-1}}C={{\sin }^{-1}}\frac{3}{5}+{{\cos }^{-1}}\frac{12}{13}\] \[\Rightarrow C=\sin \left( {{\sin }^{-1}}\frac{3}{5}+{{\cos }^{-1}}\frac{12}{13} \right)\] using, \[\sin (A+B)=\sin A\,\,\cos B+\cos A\,\sin B\] \[\Rightarrow \,\,C=\frac{3}{5}\times \frac{12}{13}+\sqrt{1-\frac{9}{25}}\sqrt{1-\frac{144}{169}}\]\[\Rightarrow C=\frac{56}{65}\].
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