tan(a+b)=2/5 tan(b-45`)=1/4 则sin(a+45`)sin(45`-a)=?哇~两个不同答案啊？。我需要正确的。

tan(a+45)
=tan[(a+b)-(b-45)]
=[tan(a+b)-tan(b-45)]/[1+tan(a+b)tan(b-45)]
=3/22
sin(a+45)/cos(a+45)=tan(a+45)=3/22
sin(a+45)=(3/22)cos(a+45)
代入sin²(a+45)+cos²(a+45)=1
所以cos²(a+45)=484/493
原式=sin(a+45)*cos[90-(45-a)]
=sin(a+45)cos(a+45)
=(3/22)cos(a+45)*cos(a+45)
=3/22*cos²(a+45)
=3/22*484/493
=66/493

tan(a+b)=(2/5)*tan(b-45)=1/4
tan(b-45)=5/8=(tanb-1)/(1+tanb)
5tanb+5=8tanb-8
3tanb=13,tanb=13/3
(tana+13/3)*4=1-(13/3)tana
4tana+(13/3)tana=1-52/3
tana=-49/52
tan(a+45)=(tana+1/(1-tana)
tan(a-45)=(tana-1)/(1+tana)
tan(a+45)*tan(a-45)=-1=sin(a+45)sin(a-45)/[cos(a+45)cos(a-45)]
sin(a+45)sin(a-45)=-cos(a+45)cos(a-45)
sin(a+45)sin(a-45)-cos(a+45)cos(a-45)
=2sin(a+45)sin(a-45)
=-[cos(a+45+a-45)=-cos2a=-2cos^2a+1
=-2/(1+tan^2a)+1
=-2/(1+49^2/52^2)+1
=(49^2+52^2-2*52^2)/(49^2+52^2)
=-3*101/5105=-3/55