判断命题真假：存在X∈R,使sinx-cosx=√3_数学解答

判断命题真假：存在X∈R,使sinx-cosx=√3

人气：217 ℃　时间：2020-09-12 12:28:22

解答

sinx-cosx
=√2(sinx*√2/2-cosx*√2/2)
=√2(sinxcosπ/4-cosxsinπ/4)
=√2sin(x-π/4)
所以最大值=√2