Q65 / 180 · KCET 2016 · Mathematics

If \( 3 \tan ^{-1} x+\cot ^{-1}=\Pi \) then \( x \) equal to

  • A
    \( 00 \)
  • Correct answer
    B
    \( 11 \)
  • C
    \( -1 \)
  • D
    \( \frac{1}{2} \)

Solution

Given that, $3 \tan ^{-1} x+\cot ^{-1} x=\pi$ $\Rightarrow 2 \tan ^{-1} x+\left(\tan ^{-1} x+\cot ^{-1} x\right)=\Pi$ Since, $\tan ^{-1} x+\cot ^{-1} x=\frac{\Pi}{2} .$ Then $\Rightarrow 2 \tan ^{-1} x+\frac{\Pi}{2}=\pi$ $\Rightarrow 2 \tan ^{-1} x=\frac{\Pi}{2}$ $\Rightarrow \tan ^{-1} x=\frac{\Pi}{4}$ $\Rightarrow x=\tan \frac{\Pi}{4}=1$

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

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