tan（α+8π/7）=tan(α+π/7)=a
sin（15π/7+α）=sin（π/7+α）
cos（α-13π/7)=cos（13π/7-α)=cos(π+6π/7-α)=-cos(6π/7-α)=-cos(π-π/7-α)=cos(π/7+α)
sin（20π/7-α)=sin（6π/7-α)=sin（π-π/7-α)=sin(π/7+α)
cos（α+22π/7)=cos(α+8π/7)=-cos(π/7+α)
所以
[ sin（15π/7+α）+3cos（α-13π/7）]/[sin（20π/7-α）-cos（α+22π/7）]=
[sin（π/7+α）+3cos(π/7+α)]/[sin(π/7+α)+cos(π/7+α)]
=1+2cos(π/7+α)/[sin(π/7+α)+cos(π/7+α)]
因為[sin(π/7+α)+cos(π/7+α)]/2cos(π/7+α)=(1/2)*tan(α+π/7)+1/2=(a+1)/2
所以2cos(π/7+α)/[sin(π/7+α)+cos(π/7+α)]=2/(a+1)
因此原式=1+2/(a+1)