设
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