已知f(x)=2根号3cos^2
f(x)=2√3(cosx)^2-2sinxcosx-√3
=√3[2(cosx)^2-1]-sin2x
=√3cos2x-sin2x
=2(√3/2cos2x-1/2sin2x)
=2sin(π/3-2x)
=2sin(2x+2π/3)
2kπ-π/2f(x)=2sin[2(x+π/3)+2π/3]
=2sin(2x+4π/3)=2sin(2x-2π/3)
—>g(x)=2sin(4x-2π/3)
(3)x∈[-π/8,π/8],2x∈[-π/4,π/4],2x+2π/3∈[5π/12,11π/12]
即正好为f(x)的一个单调增区间
sin(2x+2π/3)∈[-1,1]
f(x)=2...全部
f(x)=2√3(cosx)^2-2sinxcosx-√3
=√3[2(cosx)^2-1]-sin2x
=√3cos2x-sin2x
=2(√3/2cos2x-1/2sin2x)
=2sin(π/3-2x)
=2sin(2x+2π/3)
2kπ-π/2f(x)=2sin[2(x+π/3)+2π/3]
=2sin(2x+4π/3)=2sin(2x-2π/3)
—>g(x)=2sin(4x-2π/3)
(3)x∈[-π/8,π/8],2x∈[-π/4,π/4],2x+2π/3∈[5π/12,11π/12]
即正好为f(x)的一个单调增区间
sin(2x+2π/3)∈[-1,1]
f(x)=2sin(2x+2π/3)∈[-2,2]。
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