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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2017 · Mathematics · Inverse Trigonometric Functions

If y= ^ -1 ((x+1)/(x-1))+ ^ -1 ((x-1)/(x+1)) , then (d y)/(d x) is...

If y=sec⁡−1(x+1x−1)+sin⁡−1(x−1x+1)y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right), then dydx\frac{d y}{d x} is equal to

Options

  1. A00
  2. B11
  3. Cx−1x+1\frac{\mathrm{x}-1}{\mathrm{x}+1}
  4. Dx+1x−1\frac{\mathrm{x}+1}{\mathrm{x}-1}

Correct answer

A. 00

Step-by-step solution

y=sec⁡−1(x+1x−1)+sin⁡−1(x−1x+1)=cos⁡−1(x−1x+1)+sin⁡−1(x−1x+1)\begin{aligned} & y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right) \\ & =\cos ^{-1}\left(\frac{x-1}{x+1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)\end{aligned} =π2(∵sin⁡−1x+cos⁡−1x=π2)∴dydx=0\begin{aligned} & =\frac{\pi}{2}\left(\because \sin ^{-1} \mathrm{x}+\cos ^{-1} \mathrm{x}=\frac{\pi}{2}\right) \\ & \therefore \frac{\mathrm{dy}}{\mathrm{dx}}=0\end{aligned}
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