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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{1}{1+\cos x }$$ dx$

\[\begin {array} {1 1} (a)\;cosec x +\cot x +c \\ (b)\;-cosec x +\cot x +c \\ (c)\;\sin ^2 x+\cos x \sin x +c \\ (d)\;cosec x - \cot x +c \end {array}\]

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1 Answer

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$ \int \large\frac{1}{1+\cos x}$$dx=\int \large\frac{(1-\cos x) dx}{(1\cos x)(1- \cos x)}$
$\qquad= \int \large\frac{(1- \cos x)}{1- \cos ^2 x}$$dx$
$\int \large\frac{(1-\cos x)}{\sin^2 x}$$dx=\int \bigg[ \large\frac{1}{\sin ^2 x }-\frac{\cos x}{\sin ^2 x}\bigg]$
=>$\int (cosec^2 x- cosec x \cot x)dx$
=> $ \int cosec ^2 x dx - \int cosec x \cot x dx$
=> $- \cot x + cosec x +c$
Hence d is the correct answer
answered Dec 17, 2013 by meena.p
 
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