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Question: Answered & Verified by Expert
$2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=$
MathematicsInverse Trigonometric FunctionsJEE Main
Options:
  • A $\tan ^{-1}\left(\frac{49}{29}\right)$
  • B $\frac{\pi}{2}$
  • C $0$
  • D $\frac{\pi}{4}$
Solution:
2355 Upvotes Verified Answer
The correct answer is: $\frac{\pi}{4}$
$\begin{aligned} & 2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\tan ^{-1}\left(\frac{2(1 / 3)}{1-(1 / 9)}\right)+\tan ^{-1}\left(\frac{1}{7}\right) \\ & \quad=\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{1}{7}=\tan ^{-1}\left(\frac{(3 / 4)+(1 / 7)}{1-(3 / 4) \times(1 / 7)}\right) \\ & \quad=\tan ^{-1}\left(\frac{25}{25}\right)=\frac{\pi}{4}\end{aligned}$

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