已知cos(α+β)=0,求证tan(2α+β)=0

已知cos(α+β)=0,求证tan(2α+β)=0
已知cos(α+β)=0,求证tan(2α+β)=0

已知cos(α+β)=0,求证tan(2α+β)=0
题错了,例如α=π/3,β=π/6,则α+β=π/2,2α+β=5π/6
cos(α+β)=cos(π/2)=0,而tan(2α+β)=tan(5π/6)=-√3/3≠0