Given the function f (x) = sin square meter x + 2sinxconx cos square x, find the monotone increasing interval of function f (x)

f（x）=sin²x+2sinxcosx-cos²x
=sin2x-cos2x
=√2sin(2x-π/4)
2kπ-π/2≤2x-π/4≤2kπ+π/2
2kπ-π/4≤2x≤2kπ+3π/4
kπ-π/8≤x≤kπ+3π/8
So monotone increasing interval: [K π - π / 8, K π + 3 π / 8], K ∈ Z

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