sinα=(2√5)/5
因为α是第一象限角,所以cosα≥0
因此：cosα=√[1-(sinα)^2]
cosα=√(1-[(2√5)/5]^2}
cosα=√(1/5)
cosα=(√5)/5
tan(α+π)+[sin(5π/2+α)/cos(5π/2-α)]
=tanα+[sin(π/2+α)/cos(π/2-α)]
=sinα/cosα+cosα/sinα
=[(2√5)/5]/[(√5)/5]+[(√5)/5]/[(2√5)/5]
=2+1/2
=5/2