已知函数f(x)=2√3sinxcosx+cos^2x-sin^2x-1,若x属于[-5π/12,π/3],求值域

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已知函数f(x)=2√3sinxcosx+cos^2x-sin^2x-1,若x属于[-5π/12,π/3],求值域

已知函数f(x)=2√3sinxcosx+cos^2x-sin^2x-1,若x属于[-5π/12,π/3],求值域
已知函数f(x)=2√3sinxcosx+cos^2x-sin^2x-1,若x属于[-5π/12,π/3],求值域

已知函数f(x)=2√3sinxcosx+cos^2x-sin^2x-1,若x属于[-5π/12,π/3],求值域
f(x)=√3sin2x+cos2x-1
=2sin(2x+π/6)-1
-2π/3<2x+π/6<5π/6
所以sin能娶到-1和1
所以值域是【-3,1】

f(x)=2√3sinxcosx+cos^2x-sin^2x-1,
=√3sin2x+cos2x-1
=2sin(2x+π/6)-1
x属于[-5π/12,π/3],
2x+π/6属于[-2π/3,5π/6],
值域:[-1-√3,1]