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Question
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
Options
0
1/2
− 1
none of these
Solution
(d) none of these
We know that
\[\tan^{- 1} x + \tan^{- 1} y = \tan^{- 1} \left( \frac{x + y}{1 - xy} \right)\]
Now,
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11} = \tan^{- 1} \left( \frac{\frac{1}{11} + \frac{2}{11}}{1 - \frac{1}{11}\frac{2}{11}} \right)\]
\[ = \tan^{- 1} \left( \frac{\frac{3}{11}}{\frac{121 - 2}{121}} \right)\]
\[ = \tan^{- 1} \left( \frac{\frac{3}{11}}{\frac{119}{121}} \right)\]
\[ = \tan^{- 1} \left( \frac{33}{119} \right)\]
\[ = 0 . 27\]
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