化简:cos(π/2+α)-tan(π/2-α)sin(π/2+α)

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化简:cos(π/2+α)-tan(π/2-α)sin(π/2+α)
化简:cos(π/2+α)-tan(π/2-α)sin(π/2+α)

化简:cos(π/2+α)-tan(π/2-α)sin(π/2+α)
cos(π/2+α)-tan(π/2-α)sin(π/2+α)
=-sinα-cotαcosα
=-sinα-(cosα/sinα)cosα
=-(sin²α+cos²α)/sinα
=-1/sinα
=-cscα

cos(π/2+α)=-sinα
tan(π/2-α)=cotα=cosα/sinα
sin(π/2+α)=cosα
原式=-sinα-(cosα/sinα)*cosα
=-sin²α/sinα-cos²α/sinα=-(sin²α+cos²α)sinα=-1/sinα