A) \[{{\tan }^{-1}}\left( \frac{49}{29} \right)\]
B) \[\frac{\pi }{2}\]
C) 0
D) \[\frac{\pi }{4}\]
Correct Answer: D
Solution :
\[2{{\tan }^{-1}}\left( \frac{1}{3} \right)+{{\tan }^{-1}}\left( \frac{1}{7} \right)={{\tan }^{-1}}\left( \frac{2(1/3)}{1-(1/9)} \right)+{{\tan }^{-1}}\left( \frac{1}{7} \right)\] \[={{\tan }^{-1}}\frac{3}{4}+{{\tan }^{-1}}\frac{1}{7}={{\tan }^{-1}}\left( \frac{(3/4)+(1/7)}{1-(3/4)\times (1/7)} \right)\] \[={{\tan }^{-1}}\left( \frac{25}{25} \right)=\frac{\pi }{4}\].
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