已知sinα+cosα=1/5,且π/2≤α≤3π/4,求cos2α

显示全部楼层 · 2011-11-14 23:59:58

解：∵sinα+cosα=1/5 ==>(sinα+cosα)2=1/25
==>sin2α+cos2α+2sinαcosα=1/25
==>1+sin(2α)=1/25
∴sin(2α)=-24/25
∵π/2≤α≤3π/4 ==>π≤2α≤3π/2
∴cos(2α) - cosasinα+cosα=1/5,cosa * cosa +sina * sina+2sina * cosa=1/25;2sina * cosa=-24/25cosa * cosa +sina * sina-2sina * cosa=49/2...

千问 · 2011-11-14 23:59:58

(sinα+cosα)2=sin2α+cos2α+2sinαcosα=1+sin2α=1/25，sin2α=—24/25, sin22α+cos22α=1 故cos2α=√￣（1-sin22α）=7/25...