f(x)=cos(2X+π/3)+sin(x-π/4)sin(x+π/4)的最小正周期和图像的对称轴方程是什么？

显示全部楼层 · 2010-9-27 23:06:49

f(x)=cos(2X+π/3)+sin(x-π/4)sin(x+π/4)的最小正周期和图像的对称轴方程是什么？在【-π/12,π/2】的值域是多少？
越快越好，谢谢帮助，30分吧~
原函数应当是f(x)=cos(2X-π/3)+sin(x-π/4)sin(x+π/4)

千问 · 2010-9-27 23:06:49

解：f(x)=cos(2x+π/3)+sin(x-π/4)sin(x+π/4)
=cos(2x+π/3)+sin(x-π/4)sin(x+π/4-π/2+π/2)
=cos(2x+π/3)+sin(x-π/4)sin(x-π/4+π/2)
=cos(2x+π/3)+sin(x-π/4)cos(x-π/4)
=cos(2x+π/3)+1/2sin(2x-π/2)
=cos(2x+π/3)-1/2cos(2x)
=1/2

千问 · 2010-9-27 23:06:49

f(x)=cos(2x-π/3)+sin(x-π/4)sin(x+π/4)= cos(2x-π/3)-sin(π/4-x)sin(x+π/4)= cos(2x-π/3)-cos(x+π/4)sin(x+π/4)=(1/2)cos2x+(√3/2)sin2x-(1/2)sin(2x+π/2)=(1/2)cos2x+(√3/2)sin2x-(1/