已知函数 cos(2a-圆周率/3）+sin(a-圆周率/4)sin(a+圆周率/4) 求函数的最小正周期和图像对称轴方

Y=cos(2a-π/3）+sin(a-π/4)sin(a+π/4)
= cos(2a-π/3）+ sin(a-π/4)sin[(a-π/4)+π/2]
= cos(2a-π/3）+ sin(a-π/4)cos(a-π/4)
= cos(2a-π/3）+1/2*sin(2a-π/2)
= cos(2a-π/3）-1/2*cos(2a)
= cos(2a) cosπ/3+sin(2a)sinπ/3-1/2*cos(2a)
=√3/2* sin(2a)
函数的最小正周期为π,
令2a=kπ+π/2,k∈Z.
a=kπ/2+π/4,k∈Z.这就是图像的对称轴方程.
a∈[-π/12,π/2],
则2a∈[-π/6,π],
sin(2a) ∈[-1/2,1].
函数值域是[-√3/4,√3/2].