Search any question & find its solution
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
Options:
Solution:
1601 Upvotes
Verified Answer
The correct answer is:
$\frac{17}{6}$
$\tan \left(\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{3}\right)=\tan \left(\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{2}{3}\right)$
$=\tan \tan ^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4} \times \frac{2}{3}}\right)=\tan \tan ^{-1}\left(\frac{17}{6}\right)=\frac{17}{6}$
$=\tan \tan ^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4} \times \frac{2}{3}}\right)=\tan \tan ^{-1}\left(\frac{17}{6}\right)=\frac{17}{6}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.