cos(B-C)=cosBcosC-sinBsinC
cosA=cos[π-(B+C)]=-cos(B+C)=-cosBcosC+sinBsinC
所以cosA/cos(B-C)=(-cosBcosC+sinBsinC)/(cosBcosC-sinBsinC)
分子分母同时除以cosBcosC,有:
cosA/cos(B-C)=[-1+sinBsinC/(cosBcosC)]/[1-sinBsinC/(cosBcosC)]
=(-1+tanBtanC)/(1-tanBtanC)
现在你将条件带入即可