Search any question & find its solution
Question:
Answered & Verified by Expert
$2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=$
Options:
Solution:
2355 Upvotes
Verified Answer
The correct answer is:
$\frac{\pi}{4}$
$\begin{aligned} & 2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\tan ^{-1}\left(\frac{2(1 / 3)}{1-(1 / 9)}\right)+\tan ^{-1}\left(\frac{1}{7}\right) \\ & \quad=\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{1}{7}=\tan ^{-1}\left(\frac{(3 / 4)+(1 / 7)}{1-(3 / 4) \times(1 / 7)}\right) \\ & \quad=\tan ^{-1}\left(\frac{25}{25}\right)=\frac{\pi}{4}\end{aligned}$
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.