已知sinA是sin C和cosC的等差中项,sinB是sinC和cosC的等比中项,求证：2cos2A=cos2B.

2sinA=sinC+cosC (1)
(sinB)^2=sinCcosC (2)
将（1）式平方
4(sinA)^2=(sinC)^2+(sinC)^2+2sinCcosC
=1+2(sinB)^2
左右两式加负号
-4(sinA)^2=-1-2(sinB)^2
再将左右两式加2
2-4(sinA)^2=1-2(sinB)^2
2（1-2(sinA)^2）=1-2(sinB)^2
2cos2A=cos2B

2sinA=sin C+cosC (1)
sinB^2=sinCcosC (2)
(1)^2-2(2)
4sin^2A-2sinB^2=sin^2A+cos^2A
4sin^2A-2sinB^2=1
1-2sinB^2=2(1-2sin^2A)
2cos2A=cos2B
的证

(sinC+cosC)/2=sinA;sinB/sinC=cosC/sinB;
顺序分析法：2cos2A=cos2B；
2（1-2sinA^2）=1-2sinB^2
2[1-2((sinC+cosC)/2)^2]=1-2sinB^2
2-(sinC^2+cosC^2+2sinC*cosC)=1-2sinC*cosC
1=1;
是正确的；
然后求证的时候逆推回去就好了