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  • The value of  <img alt="\tan \left [ \cos ^{-1}\left ( \frac{4}{5} \right )+\tan ^{-1}\left ( \frac{2}{3} \right ) \right ]" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Ctan%20%5Clef

The value of  \tan \left [ \cos ^{-1}\left ( \frac{4}{5} \right )+\tan ^{-1}\left ( \frac{2}{3} \right ) \right ] is

Option: 1

\frac{6}{17}


Option: 2

\frac{7}{16}


Option: 3

\frac{16}{7}


Option: 4

None of these


Answers (1)

best_answer

Since \cos ^{-1}\left ( \frac{4}{5} \right )=\tan ^{-1}\left ( \frac{3}{4} \right )

\therefore \tan \left [ \cos ^{-1}\left ( \frac{4}{5} \right )+\tan ^{-1}\left ( \frac{2}{3} \right ) \right ]

=\tan \left [ \tan ^{-1}\frac{3}{4}+\tan ^{-1}\frac{2}{3}\right ]=\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}}=\frac{17}{6}

Posted by

seema garhwal

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