Q64 / 160 · AP EAMCET 2024 (18 May Shift 1) · Mathematics

$\tan ^{-1} 2+\tan ^{-1} 3=$

  • A
    $-\frac{\pi}{4}$
  • B
    $\frac{\pi}{4}$
  • Correct answer
    C
    $\frac{3 \pi}{4}$
  • D
    $\frac{5 \pi}{4}$

Solution

$\begin{aligned} & \text { Since, } \tan ^{-1} 2+\tan ^{-1}(3) \\ = & \pi+\tan ^{-1}\left(\frac{2+3}{1-2 \times 3}\right)=\pi+\tan ^{-1}\left(\frac{5}{-5}\right)\end{aligned}$ $=\pi+\tan ^{-1}(-1)=\pi-\frac{\pi}{4}=\frac{3 \pi}{4}$

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

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