A) 1
B) 3
C) 4
D) 5
Correct Answer: B
Solution :
\[\because \]\[{{\sin }^{-1}}\left( \frac{x}{5} \right)+\cos e{{c}^{-1}}\left( \frac{5}{4} \right)=\frac{\pi }{2}\] \[\Rightarrow \]\[{{\sin }^{-1}}\left( \frac{x}{5} \right)+{{\sin }^{-1}}\left( \frac{4}{5} \right)=\frac{\pi }{2}\] \[\Rightarrow \]\[{{\sin }^{-1}}\left( \frac{x}{5} \right)=\frac{\pi }{2}-{{\sin }^{-1}}\left( \frac{4}{5} \right)\] \[\Rightarrow \]\[{{\sin }^{-1}}\left( \frac{x}{5} \right)={{\cos }^{-1}}\left( \frac{4}{5} \right)\] \[\Rightarrow \]\[{{\sin }^{-1}}\left( \frac{x}{5} \right)=si{{n}^{-1}}\left( \frac{3}{5} \right)\] \[\Rightarrow \]\[x=3\]
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