x1,x2是方程的两个根,由韦达定理得
x1+x2=sin(π/5)
x1x2=cos(4π/5)
设A=arctanx1,B=arctanx2
则tanA=x1,tanB=x2
tan(A+B)
=(tanA+tanB)/(1-tanAtanB)
=(x1+x2)/(1-x1x2)
=sin(π/5)/cos(4π/5)
=sin(π-π/5)/cos(4π/5)
=sin(4π/5)/cos(4π/5)
=tan(4π/5)
所以A+B=4π/5
X^2-Xsin(π/5)+cos(4π/5)=0不给过程不要紧,