己知函数f(x)=-cos2xcos5派除4+sin2xsin9派除4

己知函数f(x)=-cos2xcos5派除4+sin2xsin9派除4

f(x) = -cos2xcos5π/4+sin2xsin9π/4
= -cos2xcos(π+π/4)+sin2xsin(2π+π/4)
= cos2xcosπ/4+sin2xsinπ/4
= sin(2x+π/4)

2x+π/4属于（2kπ-π/2，2kπ+π/2）时单调增；2x+π/4属于（2kπ+π/2，2kπ+3π/2）时单调减
单调增区间：（kπ-3π/8，kπ+π/8）
单调增区间：（kπ+π/8，kπ+5π/8）
最小正周期2π/2=π
最大值1
最小值-1

令sin xcos x=t，t∈[-1/2,1/2]

sinx+cosx=√(sin^2 x + cos^2 x +2cosxsinx)

=√(1+2t)∈[0,√2]

sin x+cos x+sin xcos x

=√(1+2t)+t

值域为[-1/2,√2+1/2]