已知tan(α+β)=2/5,tan(β-π/4)=1/4,试求cos(α-π/4)

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已知tan(α+β)=2/5,tan(β-π/4)=1/4,试求cos(α-π/4)
已知tan(α+β)=2/5,tan(β-π/4)=1/4,试求cos(α-π/4)

已知tan(α+β)=2/5,tan(β-π/4)=1/4,试求cos(α-π/4)

tan(a+派/4)=x
tan(a+b)=(x+1/4)/(1-x/4)
2/5=(4x+1)/(4-x)
8-2x=20x+5
22x=3
x=3/22
tan(a+派/4)=3/22
tan(派/2-a-派/4)=22/3
tan(派/4-a)=22/3
tan(a-派/4)=22/3
sec^2(a-派/4)=(9+22^2)/9=493/9
cos^2(a-派/4)=9/493
cos(a-派/4)=正负3/(493)^0.5
493=17*29没法约
,分母有理化只能是正负3根号493/493