sinx-cosx=1的解集是

题目

sinx-cosx=1的解集是

答案

sinx-cosx=1
√2sin(x-π/4)=1
sin(x-π/4)=√2/2
x-π/4=π/4+2kπ或3π/4+2kπ,k∈Z
解得
x=π/2+2kπ或π+2kπ,k∈Z
解集是{x|x=π/2+2kπ或π+2kπ,k∈Z}