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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Differentiation

NDA 2018 · Mathematics · Differentiation

What is d 1- 2 x dx equal to, where (π)/(4) < x < (π)/(2) ?

What is d1−sin⁡2xdx\frac{\mathrm{d} \sqrt{1-\sin 2 \mathrm{x}}}{\mathrm{dx}} equal to, where π4<x<π2\frac{\pi}{4} < \mathrm{x} < \frac{\pi}{2} ?

Options

  1. Acos⁡x+sin⁡x\cos x+\sin x
  2. B−(cos⁡x+sin⁡x)-(\cos x+\sin x)
  3. C±(cos⁡x+sin⁡x)\pm(\cos x+\sin x)
  4. DNone of the above

Correct answer

A. cos⁡x+sin⁡x\cos x+\sin x

Step-by-step solution

 For  π4<x<π21−sin⁡2x=(sin⁡2x+cos⁡2x+2sin⁡x⋅cos⁡x)1/2=(sin⁡x−cos⁡x)Differentiation =cos⁡x+sin⁡x\begin{aligned} & \text{\text{ For } } \frac{\pi}{4} < x < \frac{\pi}{2} \\ & \sqrt{1-\sin 2 x}=\left(\sin ^2 x+\cos ^2 x+2 \sin x \cdot \cos x\right)^{1 / 2} \\ & =(\sin x-\cos x) \\ & \text{Differentiation }=\cos x+\sin x\end{aligned}
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