已知向量a=(sinx,2√3sinx),b=(cosx,sinx),定义f(x)=a*b-√3 (1)求函数y=f(x),x∈R的单调递减区间. (2)若
f(x)=sinxcosx+2√3sin2x-√3=1/2sin2x-√3cos2x=sin(2x-π/3)(1)单调增区间：x∈(kπ-π/12，kπ+5π/12]单调...
f(x)=sinxcosx+2√3sin2x-√3
=1/2sin2x-√3cos2x
=sin(2x-π/3)
(1)单调增区间：x∈(kπ-π/12，kπ+5π/12]
单调减区间：x∈(kπ+5π/12，kπ+11π/12]
(2)f(x+θ)=sin(2x+2θ-π/3)
0＜θ＜π/2
-π/3＜2θ-π/3＜2π/3
y=f(x+θ)(0＜θ＜π/2)为偶函数
∴2θ-π/3=π/2
θ=5π/12 展开
=1/2sin2x-√3cos2x
=sin(2x-π/3)
(1)单调增区间：x∈(kπ-π/12，kπ+5π/12]
单调减区间：x∈(kπ+5π/12，kπ+11π/12]
(2)f(x+θ)=sin(2x+2θ-π/3)
0＜θ＜π/2
-π/3＜2θ-π/3＜2π/3
y=f(x+θ)(0＜θ＜π/2)为偶函数
∴2θ-π/3=π/2
θ=5π/12 展开
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