判断真假并证明:如果(sinA)^2+(sinB)^2+(sinC)^2
问题描述:
判断真假并证明:如果(sinA)^2+(sinB)^2+(sinC)^2
答
在三角形ABC中证明(sinA)^2+(sinB)^2+(sinC)^2=2(1+cosAcosBcosC)由倍角公式:(sinA)^2+(sinB)^2+(sinC)^2=(1-cos2A)/2+(1-cos2B)/2+(1-cos2C)/2=3/2-1/2(cos2A+cos2B+cos2C) (对cos2A+cos2B用和差化积公式)=3/2-1...