A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) \[{{\cos }^{-1}}\left( \frac{4}{5} \right)\]
D) \[\pi \]
Correct Answer: A
Solution :
\[{{\sin }^{-1}}\frac{3}{5}+{{\tan }^{-1}}\frac{1}{7}={{\tan }^{-1}}\frac{3}{4}+{{\tan }^{-1}}\frac{1}{7}\] \[={{\tan }^{-1}}\left( \frac{(3/4)+(1/7)}{1-(3/4)\times (1/7)} \right)={{\tan }^{-1}}\left( \frac{25}{25} \right)={{\tan }^{-1}}1=\frac{\pi }{4}\].
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