MCQ
${\cos ^{ - 1}}\left( {\frac{{15}}{{17}}} \right) + 2{\tan ^{ - 1}}\left( {\frac{1}{5}} \right) = $
- A$\frac{\pi }{2}$
- B${\cos ^{ - 1}}\left( {\frac{{171}}{{221}}} \right)$
- C$\frac{\pi }{4}$
- ✓None of these
$ = {\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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