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Integration of (1-sinx )/(1+cosx)

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Integration of (1-sinx )/(1+cosx)

Posted by Priyanka Malik 7 years, 1 month ago

CBSE > Class 12 > Mathematics

1 answers

Dhruv G 7 years, 1 month ago

Int (1-sinx)/(1-cosx)•dx......➡in numerator sinx can be written as 2sinx/2•cosx/2......and in denominator 1-cosx can be written as 2sin^2 x/2.......➡final form: int (1-sinx/2•cosx/2)/(2sin^2x/2)•dx.......➡break lcm...➡use identity 1/sinx=cscx and cosx/sinx=cotx....➡finally you will have this form: int (1/2•csc^2 x/2-cotx/2)•dx........➡ integrate nd ur final ans➡ -1/2•cot x/2+logsinx/2+C....................(where cscx=cosecx)?

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