作业帮化简sin(x)(cos(x)+cos(3x)+cos(5x)+cos(7x))
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 04:23:24
化简sin(x)(cos(x)+cos(3x)+cos(5x)+cos(7x))
化简sin(x)(cos(x)+cos(3x)+cos(5x)+cos(7x))
化简sin(x)(cos(x)+cos(3x)+cos(5x)+cos(7x))
利用积化和差公式sinAcosB=(1/2)*[sin(A+B)+sin(A-B)]以及sin(-A)=-sinA的性质
可得
sin(x)(cos(x)+cos(3x)+cos(5x)+cos(7x))
=sinxcosx+sinxcos3x+sinxcos5x+sinxcos7x
=(1/2)[sin2x+sin4x+sin(-2x)+sin6x+sin(-4x)+sin8x+sin(-6x)]
=(1/2)sin8x
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