已知α∈(0,π/4)sin(π/4-α)=7/25 则cos2α
问题描述:
已知α∈(0,π/4)sin(π/4-α)=7/25 则cos2α
答
(√2/2)(cosα-sinα)=7/25
(cosα-sinα)^2=98/625
(cosα)^2+(sinα)^2-2sinαcosα=98/625
1-sin2α=98/625
sin2α=527/625
0cos2α=√[1-(sin2α)^2]=336/625