Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# If π 2 Then Find D D X ( √ 1 + Cos 2 X 2 ) - Mathematics

If $\frac{\pi}{2}$ then find $\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)$

#### Solution

$\sqrt{\frac{1 + \cos 2x}{2}}$
$= \sqrt{\frac{2 \cos^2 x}{2}}$
$= \sqrt{\cos^2 x}$
$= - \cos x (\because\frac{\pi}{2}<x<\pi)$
$\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)$
$= \frac{d}{dx}\left( - \cos x \right)$
$= - \left( - \sin x \right)$
$= \sin x$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 4 | Page 47