Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
$2 \tan ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=$
MathematicsInverse Trigonometric FunctionsJEE Main
Options:
  • A $\frac{\pi}{4}$
  • B $0$
  • C $\tan ^{-1}\left(\frac{5}{4}\right)$
  • D $\frac{\pi}{2}$
Solution:
1307 Upvotes Verified Answer
The correct answer is: $\frac{\pi}{2}$
$\begin{aligned} & 2 \tan ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\tan ^{-1} \frac{2 \times \frac{1}{3}}{1-\left(\frac{1}{3}\right)^2}+\cos ^{-1}\left(\frac{3}{5}\right) \\ & =\tan ^{-1}\left(\frac{\frac{2}{3}}{\frac{8}{9}}\right)+\cos ^{-1}\left(\frac{3}{5}\right) \\ & =\tan ^{-1}\left(\frac{3}{4}\right)+\cot ^{-1}\left(\frac{3}{4}\right) \\ & =\frac{\pi}{2}\end{aligned}$

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.