f(x)=(cosX+sinX)(cosX-sinX)+sinx*2cosx=cos2x+sin2x=√2sin(2x+π/庆没模4)=√2sin2(x+π/8)所以f(x)在[nπ+π/8,nπ+5π/8)上誉缓递增,[nπ-3π/察察8,nπ+π/8)上递减