已知函数f(x)=1+cos(x+π/4)-2sin2x,x∈[0,π/2],求f(x)的取值范围

f(x)=1+cos(x+π/4)+2cos(2x+π/2)
=1+cos(x+π/4)+2cos(2(x+π/4))
=1+cos(x+π/4)+2[2(cos(x+π/4))^2-1]
这样得到一个关于cos(x+π/4)的二次式,先求出cos(x+π/4)的值域,再作为而二次式的定义域来求最终的值域.