A) \[\frac{\pi }{2}\]
B) \[{{\cos }^{-1}}\left( \frac{171}{221} \right)\]
C) \[\frac{\pi }{4}\]
D) None of these
Correct Answer: D
Solution :
\[{{\cos }^{-1}}\left( \frac{15}{17} \right)+2{{\tan }^{-1}}\left( \frac{1}{5} \right)\]\[={{\cos }^{-1}}\left( \frac{15}{17} \right)+{{\cos }^{-1}}\left( \frac{1-1/25}{1+1/25} \right)\] \[={{\cos }^{-1}}\left( \frac{15}{17} \right)+{{\cos }^{-1}}\left( \frac{12}{13} \right)\] \[={{\cos }^{-1}}\left( \frac{15}{17}\times \frac{12}{13}-\sqrt{1-{{\left( \frac{15}{17} \right)}^{2}}}\sqrt{1-{{\left( \frac{12}{13} \right)}^{2}}} \right)\] \[={{\cos }^{-1}}\left( \frac{140}{221} \right)\].
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