A) \[\frac{1}{a}{{\sin }^{-1}}\left( \frac{x}{a} \right)\]
B) \[a{{\sin }^{-1}}\left( \frac{x}{a} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{x}{a} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{a}{x} \right)\]
Correct Answer: C
Solution :
\[{{\tan }^{-1}}\frac{x}{\sqrt{{{a}^{2}}-{{x}^{2}}}}={{\tan }^{-1}}\,\left( \frac{a\,\sin \theta }{a\,\cos \theta } \right)\] (Putting \[x=a\,\sin \theta )\] \[={{\tan }^{-1}}(\tan \theta )=\theta ={{\sin }^{-1}}\left( \frac{x}{a} \right)\].
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