Q66 / 150 · MHT CET 2020 (15 Oct Shift 1) · Mathematics

$2 \tan ^{-1}\left(\frac{1}{3}\right)-\tan ^{-1}\left(\frac{3}{4}\right)=$

  • Correct answer
    A
    $0$
  • B
    $2$
  • C
    $1$
  • D
    $3$

Solution

$\begin{aligned} 2 \tan ^{-1} \frac{1}{3} &=\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{3}=\tan ^{-1}\left(\frac{\frac{1}{3}+\frac{1}{3}}{1-\frac{1}{3} \times \frac{1}{3}}\right) \\ &=\tan ^{-1}\left(\frac{2}{3} \times \frac{9}{8}\right)=\tan ^{-1} \frac{3}{4} \\ \text { Now } 2 \tan ^{-1}\left(\frac{1}{3}\right)-\tan ^{-1}\left(\frac{3}{4}\right) &=\tan ^{-1}\left(\frac{3}{4}\right)-\tan ^{-1}\left(\frac{3}{4}\right)=0 \end{aligned}$

Hence, the correct answer is option: 'A'.

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