f(x)=2Cosx(Sinx-Cosx)+1(1)f(x)最小正周期要过程啊(2)求f(x)值域(3)f(x)在区间[π/8,3π/4]上最值

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f(x)=2Cosx(Sinx-Cosx)+1(1)f(x)最小正周期要过程啊(2)求f(x)值域(3)f(x)在区间[π/8,3π/4]上最值

f(x)=2Cosx(Sinx-Cosx)+1(1)f(x)最小正周期要过程啊(2)求f(x)值域(3)f(x)在区间[π/8,3π/4]上最值
f(x)=2Cosx(Sinx-Cosx)+1
(1)f(x)最小正周期要过程啊
(2)求f(x)值域
(3)f(x)在区间[π/8,3π/4]上最值

f(x)=2Cosx(Sinx-Cosx)+1(1)f(x)最小正周期要过程啊(2)求f(x)值域(3)f(x)在区间[π/8,3π/4]上最值
f(x)=2Cosx(Sinx-Cosx)+1
=2sinxcosx-2(cosx)^2+1
=sin2x-cos2x
=√2sin(2x-π/4)
(1) 最小正周期为π
(2)值域为[-√2,√2]
(3)x∈[π/8,3π/4]
则2x-π/4∈[0,5π/4]
因此sin(2x-π/4)∈[-1/√2,1]
f(x)∈[-1,√2]
f(x)最大值为√2,最小值为-1
注:√2表示根号2