化简 sin3/4x·cos3/4x·cos3/2x
问题描述：
化简 sin3/4x·cos3/4x·cos3/2x
答
3\4x(sin-cos)
答
令 y=3/2x ,则 3/4x=y/2 ,2y=3/x
由倍角公式2sinxcosx=sin2x
sin3/4x·cos3/4x·cos3/2x
=sin(y/2) * cos (y/2 )* cosy
=0.5siny*cosy
=0.25sin2y
=sin(3/x) / 4
答
sin(3x/4)cos(3x/4)cos(3x/2)
=(1/2)2sin(3x/4)cos(3x/4)cos(3x/2)
=(1/2)sin[2*(3x/4)]cos(3x/2)
=(1/2)sin(3x/2)cos(3x/2)
=(1/4)2sin(3x/2)cos(3x/2)
=(1/4)sin[2(3x/2)]
=(1/4)sin3x.
答
原式=1/2(sin3/2x·cos3/2x)·cos3/2x
=1/4sin3/x
答
【1】公式：2sinxcosx=sin2x.
【2】sin(3x/4)cos(3x/4)=[2sin(3x/4)cos(3x/4)]/2=[sin(3x/2)]/2.
【3】sin(3x/2)cos(3x/2)=[2sin(3x/2)cos(3x/2)]/2=[sin(3x)]/2.
【4】原式=[2sin(3x/4)cos(3x/4)] ×[cos(3x/2)]/2
=[2sin(3x/2)cos(3x/2)]/4
=[sin(3x)]/4.