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(sinBcosCcosBsinC)
化简为cos^2B（1-sin^2C）+cos^2C(1-sin^2B)=
2(sinBcosCcosBsinC)
1-sin^2C=cos^2C
1-sin^2B=cos^2B
所以cos^2Bcos^2C+cos^2Ccos^2B=2(sinBcosCcosBsinC)
即为2cos^2Bcos^2C=2(sinBcosCcosBsinC)
即为cosBosC=sinBsinC
cos(B+C)=0所以B+C=90度
直角三角形