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Integrate : $\int \large\frac{1}{1- \sin x }$$dx$

$(a)\;\cot x + cosec x +c \\(b)\;\tan x +\sec x+c \\(c)\;\sin x + \cos x +c \\ (d)\;None$

1 Answer

To solve this type of question multiply with $1+\sin x $ in denominator and numerator.
=> $\int \large\frac{1+\sin x }{1- \sin ^2 x }$$dx$
=> $\sec ^2 x dx +\int \sec x \tan x dx$
=> $\tan x +\sec x+c$
Hence b is the correct answer.
answered Jan 2, 2014 by meena.p