余弦定理的证明

[a691662]

其实用正弦定理也可证的： 由正弦定理我们可以知道 a/sinA=b/sinB=c/sinC=2R 代入余弦定理的左边a^2+b^2-2abcosC=4R^2(­sinA)^2+4R^2(sinB)^2-8R^2sinAs­inBcosC 所以(a^2+b^2-2abcosC)/4R^2 =(sinA)^2+(sinB)^2-2sinAsinBco­sC =(1-cos2A)/2+(1-cos2B)/2-2sinA­sinBcosC =1-(cos2A+cos2B)/2+(cos(A+B)/2­-cos(A-B)/2)cosC =1-cos(A+B)cos(A-B)+(cos(A+B)/­2-cos(A-B)/2)cosC =1+cosCcos(A-B)+(sinC/2-cos(A-­B)/2)cosC 哦,太繁了,接下来只要证明到余弦定理的右边c^2就可以了

[cutheadster]

awesome.

[BBOOBBOO2]

very good！