求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.

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求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.
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求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.
求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.

求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.
y=sin^4x+cos^4x+4sin^2xcos^2x-1
=(sin^2x+cos^2x)^2+2sin^2xcos^2x-1
=1+2sin^2xcos^2x-1
=2sin^2xcos^2x
=1/2*sin^2(2x)
=(1-cos4x)/4
=1/4-1/4*cos4x
周期T=2π/4=π/2
值域是:[0,1/2]
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