正弦函数用定义求导

题目

正弦函数用定义求导
就是用定义来求 F(x)=Sin(x)
F'(x)=Lim h->0 ( (F(x+h)-F(x))/h )

答案

lim h->0 (sin(x+h)-sin(x))/h=(sin(x)cos(h)+cos(x)sin(h)-sin(x))/h由lim h->0 sin(h)/h=1,cos(h)=1-2sin^2(h/2)带入有：=(sin(x)(1-2sin^2(h/2))+cos(x)*h-sin(x))/h=(cos(x)*h-2sin(x)*sin^2(h/2))/h又由lim h->...