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Integration of 1/(1+tanx)

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Integration of 1/(1+tanx)

    • Posted by Shreya Roy 7 years, 11 months ago

    CBSE > Class 12 > Mathematics
    • 1 answers

    Shweta Sharma 7 years, 11 months ago

    Tanx=sinx/cosx Integration of 1/1+sinx/cosx dx =integration of cosx/sinx+cosx dx Now multiply and divide by 2 1/2 integration of 2cosx/sinx+cosx 1/2integration of ( {cosx-sinx} + {cosx+sinx} )/cosx +sinx 1/2 integration of (cosx-sinx /cosx+sinx ) dx +1/2 Let cosx -sinx =t Differtiation wrt x -(cosx+sinx) = dt/dx Dx= - dt/ cosx +sinx - 1/2 integration of 1/t dt +1/2 -1/2 logt +1/2 -1/2 log |cosx -sinx| +1/2 +C

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