设f(x)=6cos^2x-根号3sin2x,求f(x)的单调增区间和单调减区间

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设f(x)=6cos^2x-根号3sin2x,求f(x)的单调增区间和单调减区间
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设f(x)=6cos^2x-根号3sin2x,求f(x)的单调增区间和单调减区间
设f(x)=6cos^2x-根号3sin2x,求f(x)的单调增区间和单调减区间

设f(x)=6cos^2x-根号3sin2x,求f(x)的单调增区间和单调减区间
f(x)=6cos^2x-根号3sin2x
=3+3cos2x-√3sin2x
=3+2√3cos(2x+π/6),
它的减区间由2kπ

f(x)=6cos²x-√3sin2x
=3(cos2x+1)-√3sin2x
=3cos2x-√3sin2x+3
=2√3cos(2x+π/6)+3
增区间:2kπ-π≤2x+π/6≤2kπ
kπ-7π/12≤x≤kπ-π/12
即增区间是:[kπ-7π/12,kπ-π/12],k...

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f(x)=6cos²x-√3sin2x
=3(cos2x+1)-√3sin2x
=3cos2x-√3sin2x+3
=2√3cos(2x+π/6)+3
增区间:2kπ-π≤2x+π/6≤2kπ
kπ-7π/12≤x≤kπ-π/12
即增区间是:[kπ-7π/12,kπ-π/12],k∈Z
减区间:2kπ≤2x+π/6≤2kπ+π
kπ-π/12≤x≤kπ+5π/12
即减区间是:[kπ-π/12,kπ+5π/12],k∈Z

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