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  1. If you mean
    1/sin2x + cos4x/sin4x
    then that is
    1/sin2x + (2cos^2 2x - 1)/(2sin2x cos2x)

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

    Not sure just what you are after

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  2. 1/sin2x+2(cos2x)^2 -1/2sin2xcos2x
    = 1/sin2x[2cos2x+2(cos2x)^2 - 1]/2cos2x
    =[2cos2x+2(cos2x)^2 -1]/sin4x

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