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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2021 · Mathematics · Inverse Trigonometric Functions

What is the slope of the tangent of y= ^ -1 ( x) at x=-(π)/(4) ?

What is the slope of the tangent of y=cos⁡−1(cos⁡x)y=\cos ^{-1}(\cos x) at x=−π4?x=-\frac{\pi}{4} ?

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

A. -1

Step-by-step solution

 Slope of  the tangent =dydxAt x=−π4,dydx(cos⁡−1(cos⁡x))=ddx(−x)\begin{aligned} & \text{ Slope\text{ of } the tangent }=\frac{d y}{d x} \\ & \text{At } x=\frac{-\pi}{4}, \frac{d y}{d x}\left(\cos ^{-1}(\cos x)\right)=\frac{d}{d x}(-x)\end{aligned}∴−π≤x≤0=dydx−1\begin{aligned} & \therefore-\pi \leq x \leq 0 \\ & =\frac{d y}{d x}-1\end{aligned}$
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