trigonometry

Prove
cotx-1/cotx+1=1-sin2x/cos2x

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  1. changing all to sinx and cosx, we have on the left:

    (cos/sin - 1)/(cos/sin + 1)
    = (cos-sin)/sin / (cos+sin)/sin
    = (cos-sin)/(cos+sin)
    = (cos-sin)^2 / (cos^2-sin^2)
    = (cos^2 - 2sin*cos + sin^2)/(cos^2-sin^2)
    = (1-sin2x)/cos2x

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