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Home  >>  CBSE XII  >>  Math  >>  Integrals
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$\int\;\large\frac{1}{1+cos x} \;dx$

$(a)\;tan(\large\frac{x}{2})+c\qquad(b)\;sec^2(\large\frac{x}{2})+c\qquad(c)\;\large\frac{1}{2}tan(\large\frac{x}{2})+c\qquad(d)\;2tan(\large\frac{x}{2})+c$

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1 Answer

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Answer : (a) $\;tan(\large\frac{x}{2})+c$
Explanation : Using trignomentry property
$cos2\theta=2cos^2\theta-1$
$cos\theta=2cos^2\theta/2-1$
$\int \;\large\frac{1}{1+2\;cos^{2}\large\frac{x}{2}-1}=\int\; \large\frac{1}{2\;cos^2\large\frac{x}{2}}\;dx$
$=\large\frac{1}{2}\int\;sec^2(\large\frac{x}{2})\;dx$
$=\large\frac{1}{2}\int\;tan(\large\frac{x}{2})x^2+c$
$=tan(\large\frac{x}{2})+c\;.$
answered Jan 24, 2014 by yamini.v
 
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