化简fx=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/29 07:38:10

化简fx=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
求最小正周期和对图像的称轴方程

fx=cos(2x-@/)+2sin(x-@/4)sin(x+@/4)
=cos2xcos@/3+sin2xsin@/3+2(sinxcos@/4-sin@/4cosx)(sinxcos@/4+sin@/4cosx)
=cos2xcos@/3+sin2xsin@/3+2(sin平方xcos平方@/4-sin平方@/4cos平方x)
=根3/2sin2x-cos2x/2=sin(2x-@/6)
故T=2@/2=@
对称方程
由k@-@/2=2x-@/6
(k?n)
x=k@/2+@/3

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