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Integrate: (1-cosx ) cosec^2x

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Solution: We have ,

               I= int (1-cos x) cosec^2 xhspace0.1cmdx

           We know ,    sin^2 x=1-cos^2x

             I=int frac(1-cos x)sin^2 xdx=int frac(1-cos x)(1-cos^2x)dx

        Rightarrow I=int frac11+cos xdx=int frac11+2cos^2fracx2-1dx

        Rightarrow I=frac12int sec^2fracx2dx= an fracx2+c

Posted by

Deependra Verma

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