数学已知函数f(x)=sin(x+θ）+cos（x+θ)的定义域为R.（1）当θ=π/2时,求f(x)的单调递增区间.

f(x)=sin(x+θ）+cos（x+θ)
= √2[√2/2sin(x+θ)+√2/2cos(x+θ)]
=√2[sin(x+θ)cosπ/4+cos(x+θ)sinπ/4]
=√2sin(x+θ+π/4)
当 θ=π/2时,f(x) =√2sin(x+θ+π/4)
=√2sin(x+3π/4)
当 x+3π/4 ∈[2kπ-π/2,2kπ+π/2]时,f(x)单调递增；
此时 x ∈[2kπ-5π/4,2kπ-π/4] 其中 k ∈Z.