∵tanα,tanβ是方程6χ²－5χ+1=0的两根∴根据韦边定理,得 tanα+tanβ=5/6,tanα*tanβ=1/6从而 tan(α+β)=(tanα+tanβ)/(1-tanα*tanβ)=5/6/(1-1/6)=5/6/(5/6) ...是的！因为α+β=5π/4；原式子sin²（α+β）-cos（α+β）sin(α+β)-3cos²(α+β）=sin²π/4-cosπ/4*sinπ/4-3cos²π/4=-2*1/2=-1