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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS2 Marks
Question
Evalute the following integrals:
$\int\sqrt{\frac{1+\cos2\text{x}}{1-\cos2\text{x}}}\text{dx}$
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Answer

$\int\sqrt{\frac{1+\cos2\text{x}}{1-\cos2\text{x}}}\text{dx}$
$=\int\sqrt{\frac{2\cos^2\text{x}}{2\sin^2\text{x}}}\text{dx}$
$=\int\cot\text{x dx}$
$=\text{ln}|\sin\text{x}|+\text{C}$

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