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.

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