设函数f（x）=2分之根号2cos（2x+4分之兀）+sin平方x,设函数g（x）对任意x...

f（x）=（√2/2）cos（2x+π/4）+（sinx）^2
=(1/2)(cos2x-sin2x+1-cos2x)
=(1/2)(1-sin2x),
由g(x+π/2)=g(x)知π/2是g(x)的周期,
x∈[0,π/2]时,g（x）=1/2-f（x）=（1/2）sin2x,
x∈[-π/2,0]时x+π/2∈[0,π/2],g(x)=g(x+π/2)=(1/2)sin2(x+π/2)=(1/2)sin(2x+π)=(-1/2)sin2x,
同理,x∈[-π,-π/2]时g(x)=(1/2)sin2x.