cos(α+π/4)=4/5求cosα?

cos(α+π/4)=4/5
cosαcosπ/4 - sinαsinπ/4=4/5
根号2/2 cosα - 根号2/2sinα = 4/5
cosα - sinα = 4根号2/5
cosα - 4根号2/5 = sinα
cos^2α - 8根号2/5cosα + 32/25 = sin^2α
cos^2α - 8根号2/5cosα + 32/25 = 1-cos^2α
cos^2α - 4根号2/5cosα + 7/50 = 0
（cosα-根号2/10）（cosα-7根号2/10）=0
cosα=根号2/10,或7根号2/10

cosα=cos(α+π/4-π/4)=cos(α+π/4)cosπ/4+sin(α+π/4)sinπ/4
=[4/5±3/5]*根号2/2=7根号2/10 ，或根号2/10