a=180-b-c
cosa=cos(180-b-c)=-cos(b+c)=-cosbcosc+sinbsinc
cosb*cosc=1/2(1-cosa)
得cosbcosc=(1/2)[1-(-cosbcosc+sinbsinc)]
=(1/2)[1+cosbcosc-sinbsinc]
=(1/2)+(1/2)cosbcosc-(1/2)sinbsinc
移项得(1/2)cosbcosc+(1/2)sinbsinc=(1/2)
既(1/2)cos(b-c)=(1/2)
cos(b-c)=1
b-c=0 b=c
是等腰三角形
好好学习