Question

划线的部分怎么出来的

划线的部分怎么出来的 高数

Answer 1

1-cosx=1-{[cos(x/2)]^2-[sin(x/2)]^2}
=1-[cos(x/2)]^2+[sin(x/2)]^2
=[sin(x/2)]^2+[sin(x/2)]^2
=2[sin(x/2)]^2
又 sin(x/2)<x/2
所以 2[sin(x/2)]^2<2(x/2)^2

Answer 2

Let f(x)=x-sinx
f'（x）=1-cosx>=0， f(x)是增函数
f(0)=0
if x>0， then f(x)>0

x>sinx
(x/2)^2>(sin (x/2) )^2