verfying trig identity

1+Cosx 1-Cosx
_______ - _______ = 4CotxCscx

1-cosx 1+Cosx

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  1. LS = (1+cosx)/(1-cosx) - (1-cosx)/(1+cosx)
    = ((1+cosx)(1+cosx) - (1-cosx)(1-cosx)/((1-cosx)(1+cosx))
    = (1 + 2cosx + cos^2x - 1 + 2cosx - cos^2x)/(1-cos^2x)
    = 4cosx/sin^2x
    = 4(cosx/sinx)(1)/sinx
    = 4cotx cscx
    = RS

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