△ABC中求证sin^A+sin^B+sin^c≤9/4RT
问题描述：
△ABC中求证sin^A+sin^B+sin^c≤9/4
RT
答
sin^2A+sin^2B+sin^2C=(1-cosA)/2 +(1-cosB)/2 +(1-cos^2C) =2-cos(A+B)cos(A-B)-cos^2C =2+cosCsoc(A-B)-cos^2C≤2+|cosC|-cos^2C=-(|cosC|-1/2)^2+9/4 当cosC=1/2时,（即A=B=C=60°）有最大值9/4 ∴(sinA)^2+(sinB...