y=7-4sin xcos x+4cos^2 x-4cos^4 x的最大值和最小值?
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y=7-4sin xcos x+4cos^2 x-4cos^4 x的最大值和最小值?
y=7-4sin xcos x+4cos^2 x-4cos^4 x的最大值和最小值?
y=7-4sin xcos x+4cos^2 x-4cos^4 x的最大值和最小值?
y=7-4sin xcos x+4cos^2 x-4cos^4 x
= 7 - 2sin 2x + 4cos^2x(1 - cos^2x)
= 7 - 2sin 2x + 4cos^2x sin^2 x
= 7 - 2sin 2x + sin^2(2x)
=(sin 2x -1)^2 + 6
所以当sin 2x = 1 时,有最小值 6
当sin 2x = -1时,有最大值10
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