Question

\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\]  is equal to

 

 

Options

• 0

• 1/2

• − 1

• none of these

Answer 1

(d) none of these

We know that 
\[\tan^{- 1} x + \tan^{- 1} y = \tan^{- 1} \left( \frac{x + y}{1 - xy} \right)\]
Now,
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11} = \tan^{- 1} \left( \frac{\frac{1}{11} + \frac{2}{11}}{1 - \frac{1}{11}\frac{2}{11}} \right)\]
\[ = \tan^{- 1} \left( \frac{\frac{3}{11}}{\frac{121 - 2}{121}} \right)\]
\[ = \tan^{- 1} \left( \frac{\frac{3}{11}}{\frac{119}{121}} \right)\]
\[ = \tan^{- 1} \left( \frac{33}{119} \right)\]
\[ = 0 . 27\]