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Question: Answered & Verified by Expert
The value of $\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)$ is
MathematicsInverse Trigonometric FunctionsJEE Main
Options:
  • A $\frac{6}{17}$
  • B $\frac{7}{16}$
  • C $\frac{16}{7}$
  • D $\frac{17}{6}$
Solution:
1601 Upvotes Verified Answer
The correct answer is: $\frac{17}{6}$
$\tan \left(\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{3}\right)=\tan \left(\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{2}{3}\right)$
$=\tan \tan ^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4} \times \frac{2}{3}}\right)=\tan \tan ^{-1}\left(\frac{17}{6}\right)=\frac{17}{6}$

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