Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If π 2 Then Find D D X ( √ 1 + Cos 2 X 2 ) - Mathematics

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

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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
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