已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/2) 化简为sin的形式
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/06 03:45:23
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/2) 化简为sin的形式
利用三角函数积化和差及和差化积公式,
f(x)=cos(2x-π/3)-[cos(x-π/4+x+π/2)-cos(x-π/4-x-π/2)]
=cos(2x-π/3)-[cos(2x+π/4)-cos(-3π/4)]
=cos(2x-π/3)-cos(2x+π/4)+cosπ/4
=-2sin[(2x-π/3+2x+π/4)/2]sin[(2x-π/3-2x-π/4)/2]+√2/2
=-2sin(2x-π/24)sin(-7π/24)+√2/2
=2sin(2x-π/24)sin(7π/24)+√2/2.
f(x)=cos(2x-π/3)-[cos(x-π/4+x+π/2)-cos(x-π/4-x-π/2)]
=cos(2x-π/3)-[cos(2x+π/4)-cos(-3π/4)]
=cos(2x-π/3)-cos(2x+π/4)+cosπ/4
=-2sin[(2x-π/3+2x+π/4)/2]sin[(2x-π/3-2x-π/4)/2]+√2/2
=-2sin(2x-π/24)sin(-7π/24)+√2/2
=2sin(2x-π/24)sin(7π/24)+√2/2.
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