Question

The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]

 

पर्याय

• `19/8`

• `8/19`

• `19/12`

• `3/4`

Answer 1

\[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right) = \tan\left( \tan^{- 1} \frac{\sqrt{1 - \frac{9}{25}}}{\frac{3}{5}} + \tan^{- 1} \frac{1}{4} \right)\]
\[ = \tan\left( \tan^{- 1} \frac{\frac{4}{5}}{\frac{3}{5}} + \tan^{- 1} \frac{1}{4} \right)\]
\[ = \tan\left( \tan^{- 1} \frac{4}{3} + \tan^{- 1} \frac{1}{4} \right)\]
\[ = \tan\left( \tan^{- 1} \frac{\frac{4}{3} + \frac{1}{4}}{1 - \frac{1}{3}} \right)\]
\[ = \frac{\frac{16 + 3}{12}}{\frac{2}{3}}\]
\[ = \frac{19}{8}\]

Hence, the correct answer is option (a).