f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值

f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值
f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值

f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值
f(x)=1-cos2(π/4+x)-√3cos2x
=1-cos(π/2+2x)-√3cos2x
=sin2x-√3cos2x+1
=2(1/2sin2x-√3/2cos2x)+1
=2sin(2x-π/3)+1
sin(2x-π/3)=1的时候,f(X)最大值=2+1=3
sin(2x-π/3)=-1的时候,f(X)最小值=-2+1=-1