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已知函数f(x)=cos(2x减去三分之派)加二乘以shn(x减四分之派)乘cos(x减四分之派)求函数f(x)的最小正周期

题目详情
已知函数f(x)=cos(2x减去三分之派)加二乘以shn(x减四分之派)乘cos(x减四分之派)
求函数f(x)的最小正周期
▼优质解答
答案和解析
f(x)= cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)
= cos(2x-π/3)+ sin(2x-π/2)
= cos(2x-π/3)-cos(2x)
= cos(2x) cosπ/3+sin(2x)sinπ/3-cos(2x)
=1/2* cos(2x)+√3/2* sin(2x) -cos(2x)
=-1/2* cos(2x)+√3/2* sin(2x)
=sin(-π/6)cos(2x)+ cos(-π/6)sin(2x)
=sin(-π/6+2x)
=sin(2x-π/6)
最小正周期是T=2π/2 =π