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If π 2 < X < 3 π 2 , Then Write the Value of √ 1 + Cos 2 X 2 - Mathematics

Short Note

If  \[\frac{\pi}{2} < x < \frac{3\pi}{2}\] , then write the value of \[\sqrt{\frac{1 + \cos 2x}{2}}\]

 

 

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Solution

\[\because \frac{\pi}{2} < x < \frac{3\pi}{2}\]
\[ \therefore \sqrt{\frac{1 + \cos2x}{2}} = \sqrt{\frac{2 \cos^2 x}{2}} = \left| \text{ cos } x \right|\]
\[\text { In second quadrant } \text{ cos } x \text{ is negative }  . \]
\[ \therefore \sqrt{\frac{1 + \cos2x}{2}} = - \text{ cos } x\] 

Concept: Values of Trigonometric Functions at Multiples and Submultiples of an Angle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 9 Values of Trigonometric function at multiples and submultiples of an angle
Q 3 | Page 42
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