Q62 / 150 · MHT CET 2021 (21 Sep Shift 1) · Mathematics

If $y=\operatorname{cosec}^1\left[\frac{\sqrt{x}+1}{\sqrt{x-1}}\right]+\cos ^{-1}\left[\frac{\sqrt{x}-1}{\sqrt{x}+1}\right]$, then $\frac{d y}{d x}=$

  • Correct answer
    A
    0
  • B
    1
  • C
    $\frac{2}{\sqrt{x}+1}$
  • D
    $\frac{1}{2(\sqrt{\mathrm{x}}+1)}$

Solution

$$ \begin{aligned} & y=\operatorname{cosec}^{-1}\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}\right)+\cos ^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)=\sin ^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)+\cos ^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)=\frac{\pi}{2} \\ & \therefore \frac{d y}{d x}=0 \end{aligned} $$

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

Relevant Questions