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Suppose csc(x)*sin(x) = cos(x)*cot(x) + y

then, ince csc(x) = 1/sin(x), and cot(x) = cos(x)/sin(x),

1 = cos(x)*cos(x)/sin(x) + y

so y = 1 - cos2(x)/sin(x) = 1 - [1 - sin2(x)]/sin(x) = [sin2(x) + sin(x) - 1]/sin(x)

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