sin (пи-альфа)*cos(3/2пи-альфа) ctg(пи/2+альфа)/tg(2пи-альфа)

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To simplify this expression, we will use trigonometric identities:

sin(π - α) = sin(π)cos(α) - cos(π)sin(α) = 0 - (-1)sin(α) = sin(α)cos(3/2π - α) = cos(3/2π)cos(α) + sin(3/2π)sin(α) = 0*cos(α) + (-1)sin(α) = -sin(α)ctg(π/2 + α) = 1/tan(π/2 + α) = 1/cot(α) = tan(α)tg(2π - α) = tan(2π)cos(α) - cot(2π)sin(α) = 0 - 1*0 = 0

Plugging these simplifications back into the expression:

sin(π - α)cos(3/2π - α) ctg(π/2 + α) / tg(2π - α)
= sin(α)(-sin(α)) tan(α) / 0
= -sin^2(α) * tan(α) / 0

Since the denominator is 0, the expression is undefined.