tanα=-2 -> sinα/cosα=-2 -> sinα=-2cosα
sinα^2+cosα^2=1 -> (-2cosα)^2+cosα^2=1 -> cosα^2=1/5
又因为0<α<π,且tanα=-2
所以α为第二象限角
故sinα>0,cosα<0 -> cosα=-√5/5,sinα=-2cosα=2√5/5
(1)sin(α+π/6)=sinαcosπ/6+cosαsinπ/6=(2√15-√5)/10
(2)2cos(π/2+α)-cos(π-α)sin(π/2-α)-3sin(π+α)
=-2sinα+cosαcosα+3sinα
=sinα+cosα^2=(1+2√5)/5
(3)2sinα^2-sinαcosα+cos^α
=1+sinα^2-sinαcosα
=7/5