sin(2.5x)/2sin(0.5x)的最小值,0

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sin(2.5x)/2sin(0.5x)的最小值,0
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sin(2.5x)/2sin(0.5x)的最小值,0
sin(2.5x)/2sin(0.5x)的最小值,0

sin(2.5x)/2sin(0.5x)的最小值,0
设0.5x＝A,0

sin5a=sin(4a+a)=sin4acosa+cos4asina
=2sin2acos2acosa+[2(cos2a)^2-1]sina
=4sina(1-sina^2)(1-2sina^2)+2(1-2sina^2)^2 sina-sina
...

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sin5a=sin(4a+a)=sin4acosa+cos4asina
=2sin2acos2acosa+[2(cos2a)^2-1]sina
=4sina(1-sina^2)(1-2sina^2)+2(1-2sina^2)^2 sina-sina
=4sina(2sina^4-3sina^2+1)+(2-8sina^2+8sina^4)sina-sina
=8sina^5-12sina^3+4sina+2sina-8sina^3+8sina^5-sina
=16sina^5-20sina^3+5sina
sin(5x/2)/2sin(x/2)
=8(sinx/2)^4-10(sinx/2)^2+5/2
=2[2sin(x/2)^2 -5/4]^2+5/2-25/8
=2[2sin(x/2)^2-5/4]^2-5/8
sin(2.5x)/2sin(x/2)最小值 -5/8

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