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InterviewSolution
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The value of \(2 \tan^{-1} \frac 2 3 + \cos^{-1} \frac {12} {13}\) is:1. π / 22. π3. π / 44. π / 3 |
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Answer» Correct Answer - Option 1 : π / 2 \(2{\tan ^{ - 1}}\left( {\frac{2}{3}} \right) + {\cos ^{ - 1}}\left( {\frac{{12}}{{13}}} \right)\) \( = {\tan ^{ - 1}}\left( {\frac{2}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{2}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{5}{{12}}} \right)\;\) \(= {\tan ^{ - 1}}\left[ {\frac{{\frac{2}{3} + \frac{2}{3}}}{{1 - \frac{2}{3} \times \frac{2}{3}}}} \right] + {\tan ^{ - 1}}\left( {\frac{5}{{12}}} \right)\) \( = {\tan ^{ - 1}}\left[ {\frac{{\frac{4}{3}}}{{1 - \frac{4}{9}}}} \right] + {\tan ^{ - 1}}\left( {\frac{5}{{12}}} \right)\;\) \( = {\tan ^{ - 1}}\left[ {\frac{{\frac{4}{3}}}{{\frac{5}{9}}}} \right] + {\tan ^{ - 1}}\left( {\frac{5}{{12}}} \right)\) \( = {\tan ^{ - 1}}\left[ {\frac{{36}}{{15}}} \right] + {\tan ^{ - 1}}\left[ {\frac{5}{{12}}} \right]\) \( = {\tan ^{ - 1}}\left[ {\frac{{12}}{5}} \right] + {\tan ^{ - 1}}\left[ {\frac{5}{{12}}} \right]\) \( = {\tan ^{ - 1}}\left[ {\frac{{12}}{5}} \right] + {\cot ^{ - 1}}\left[ {\frac{{12}}{5}} \right]\) \( = \frac{\pi }{2}\left[ {{{\tan }^{ - 1}}x + {{\cot }^{ - 1}}x = \frac{\pi }{2}} \right]\) |
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