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If π 2 < X < π , Then Write the Value of √ 1 − Cos 2 X 1 + Cos 2 X .

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Question

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

 

 

Short/Brief Note
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Solution

We have,

\[\begin{array}{rcl}\sqrt{\frac{1 - \cos2x}{1 + \cos2x}}  =  \sqrt{\frac{2 \sin^2 x}{2 \cos^2 x}}  =  \frac{\left| \text{ sin } x \right|}{\left| \text{ cos } x \right|} =  \frac{\text{ sin } x}{- \text{ cos } x} \left( \because \frac{\pi}{2} < x < \pi \right)  =  - \text{ tan } x\end{array}\]
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle
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Chapter 9: Values of Trigonometric function at multiples and submultiples of an angle - Exercise 9.4 [Page 42]

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R.D. Sharma Mathematics [English] Class 11
Chapter 9 Values of Trigonometric function at multiples and submultiples of an angle
Exercise 9.4 | Q 5 | Page 42

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