在三角形ABC中,cos^2A+cos^2B+cos^2C=1,则三角形的形状是?cos^2B+cos^2C-(sin^2Bcos^2C+cos^2Bsin^2C)=2(sinBcosCcosBsinC) cos^2Bcos^2C+cos^2Ccos^2B=2(sinBcosCcosBsinC) 这两步是如何变化的?请用过程具体说明!
问题描述：
在三角形ABC中,cos^2A+cos^2B+cos^2C=1,则三角形的形状是?
cos^2B+cos^2C-(sin^2Bcos^2C+cos^2Bsin^2C)=2(sinBcosCcosBsinC)
cos^2Bcos^2C+cos^2Ccos^2B=2(sinBcosCcosBsinC)
这两步是如何变化的?请用过程具体说明!
答
cos^2A=cos^2(B+C)=1-sin^2(B+C)sin(B+C)=sinBcosC+sinCcosB所以cos^2A+cos^2B+cos^2C=cos^2B+cos^2C-(sin^2Bcos^2C+cos^2Bsin^2C)-2(sinBcosCcosBsinC) +1=1所以cos^2B+cos^2C-(sin^2Bcos^2C+cos^2Bsin^2C)=2(sinBc...