【坐等!】已知f(x)=sin2x-2sin^2x+1(1)求f(x)的最小正周期;(2)求f(x)的单调递增区间,

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【坐等!】已知f(x)=sin2x-2sin^2x+1(1)求f(x)的最小正周期;(2)求f(x)的单调递增区间,

【坐等!】已知f(x)=sin2x-2sin^2x+1(1)求f(x)的最小正周期;(2)求f(x)的单调递增区间,
【坐等!】已知f(x)=sin2x-2sin^2x+1
(1)求f(x)的最小正周期;
(2)求f(x)的单调递增区间,

【坐等!】已知f(x)=sin2x-2sin^2x+1(1)求f(x)的最小正周期;(2)求f(x)的单调递增区间,
f(x)=sin2x-2sin^2x+1
=sin2x-(1-cos2x)+1
=sin2x+cos2x
=√2sin(2x+π/4)
T=2π/2=π
2x+π/4在[2kπ-π/2,2kπ+π/2]单调递增
x在[kπ-3π/8,kπ+π/8]单调递增

f(x)=sin2x+cos2x=√2sin(2x+π/4)
最小正周期:2π/2 = π
当2x+π/4 ∈[2kπ-π/2,2kπ+π/2]时,函数单增,k∈Z
∴x∈[kπ-3/8π,kπ+π/8]