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Prove cotx-1/cotx+1 = sec2x - tan2x

I prove till cotx-1/cotx+1 =1/1+tanx - tanx/1+tanx

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  1. For this to work you must mean
    (cotx-1)/(cotx+1) = sec(2x) - tan(2x)

    LS = (cosx/sinx - 1)/(cosx/sinx +1)
    multiply top and bottom by sinx
    = (cosx - sinx)/(cosx + sinx)

    RS = 1/cos(2x) - sin(2x)/cos(2x)
    = (1 - 2sinxcosx)/(cos^2 x - sin^2 x)
    = (sin^2 x + cos^2 x - 2sinxcosx)/((cosx+sinx)(cosx-sinx))
    = (sinx - cosx)^2/( (cosx+sinx)(cosx-sinx))
    = (sinx - cosx)/(cosx + sinx)
    = LS

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