三角函数不等式的证明:在三角形ABC中,证明:sinA+sinB+sinC
问题描述:
三角函数不等式的证明:在三角形ABC中,证明:sinA+sinB+sinC
答
学了琴生不等式直接用凸函数性质做.
没学用和差化积.
sinA+sinB+sinc=2sin(A+B/2)cos(A-B/2)+2sinC/2cosC/2
=2sin(A+B/2)cos(A-B/2)+2sinC/2sin(A+B/2)
=2sin(A+B/2)cos(A-B/2)+2sin(C/2)sin(A+B/2)
=2sin(A+B/2)(cos(A-B/2)+sin(C/2))