A) \[{{\sin }^{-1}}\left( \frac{9}{5\sqrt{10}} \right)\]
B) \[{{\tan }^{-1}}\left( \frac{9}{14} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{9}{5\sqrt{10}} \right)\]
D) \[{{\tan }^{-1}}\left( \frac{9}{5\sqrt{10}} \right)\]
Correct Answer: A
Solution :
\[\cos \alpha =\frac{3}{5},\tan \beta =\frac{1}{3}\]\[\Rightarrow \]\[\tan \alpha =\frac{4}{3}\] \[\Rightarrow \]\[\tan (\alpha -\beta )=\frac{\frac{4}{3}-\frac{1}{3}}{1+\frac{4}{3}.\frac{1}{3}}=\frac{9}{13}\] \[\Rightarrow \]\[sin(\alpha -\beta )=\frac{9}{5\sqrt{10}}\]\[\Rightarrow \]\[\alpha -\beta ={{\sin }^{-1}}\left( \frac{9}{5\sqrt{10}} \right)\]
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