Question

已知函数f(x)=cos^2(x+π/12),g(x)=1+1/2sin2x (1)求函数y=f(x)图像的对称轴方程

(2)求函数h（x）=f（x）+g（x）的最小正周期和值域

Answer 1

f(x) = 1/2 cos(2x+pi/6), g(x) = 1+ 1/2 sin2x
f(x) 对称轴为2x+pi/6 = 0, 2pi, ...
x = -pi/12 +/- npi...
f(x)+g(x) = 1/2 cos2x * sqrt(3)/2 - 1/2 sin2x * 1/2 + 1 + 1/2 sin2x
= 1/2 cos2x sqrt(3)/2 + 1/2 sin2x 1/2 + 1 = 1/2 cos(2x-pi/6) + 1
最小正周期派，值域[-1/2, 3/2]