Question

证明:cosx>1-x^2/2

Answer 1

[[[1]]

易知,恒有:|x|≥|sinx|.x∈R.

两边平方,可得:

x²≥sin²x

∴可得:

(x/2)²≥sin²(x/2)

(x²/2)≥2sin²(x/2)

x²/2≥1-cosx

cosx≥1-(x²/2)