已知tanα=2.
tanα=2 sinα/cosα=2 sinα=2cosα
sin²α+cos²α=1
(2cosα)²+cos²α=1
5cos²α=1
cos²α=1/5
cos平方α-sinαcosα的值
=cos平方α-2cosαcosα
=-cos²α
=-1/5
2.若α属于（0,π/2),β属于（-π/2,0),且cos(α-β)=-根号10/10,
cos²α=1/5
α属于（0,π/2),
cosα=√5/5
sinα=2√5/5
cos(α-β)=-根号10/10
α属于（0,π/2),β属于（-π/2,0)
cos(α-β)=-根号10/10
α-β属于（π/2,π)
sin(α-β)=-3根号10/10
cosβ
=cos(α-(α-β))
=cosαcos(α-β)+sinαsin(α-β)
=√5/5*(-√10/10)+2√5/5*(3√10/10)
=5*√5/5*(√10/10)
=√2/2
β=-π/4