已知sin阿尔法-cos阿尔法=根号2,求下列各式的值

sinα-cosα=√2
(sinα-cosα)²=2
sin²α+cos²α-2sinαcosα=2
sinαcosα=-1/2
(1) tanα+cotα
=sinα/cosα+cosα/sinα
=(sin²α+cos²α)/(sinαcosα)
=1/(-1/2)=-2
(2)
sin³α-cos³α
=(sinα-cosα)(sin²α+cos²α+sinαcosα)
=√2(1-1/2)
=√2/2