Question

已知函数f(x)=cos(兀/3 +x)cos(兀/3 -x),g(x)=sin2x/2 -(1/4).求函数f(x)的最小正周期

求函数h(x)=f(x)-g(x)的最大值，并求使h(x)取得最大值的x集合

Answer 1

f(x)=cos(兀/3 +x)cos(兀/3 -x)
=cos(x + π/3)cos(x - π/3)
=(cos(x + π/3 + x - π/3) + cos(x + π/3 - x + π/3))/2 积化和差
=1/2 * (cos2x + cos (2π/3))
=1/2 cos2x+1/4
所以f(x)最小正周期T=π

Answer 2

那么g(x)是用来干什么的?

Answer 3

cosacosb=1/2{cos(a+b)+cos(a-b)}
f(x)=1/2{cos2∏/3+cos2x}
=-1/4+1/2cos2x
T=2∏/2=∏
(2)h(x)=-1/4+1/2cos2x-(sin2x/2 -1/4)
=1/2cos2x-1/2sin2x
=√2/2(2x+∏/4)
2x+∏/4=2k∏
x=k∏-∏/8

Answer 4

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