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

首页/题库/104℃/2024-07-20 04:56:44

优质解答：

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.

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