f(x)=根号3sin(wx+q)-cos(wx+q),（w>0,0<q<派）为偶函数，图象的两相邻对称轴的距离为派/2，求f(派/8)?详

f(x)=√[(√3)²+1²]*sin(wx+q-z)
=2sin(wx+q-z)
tanz=1/√3
所以z=π/6
f(x)=2sin(wx+q-π/6)
sin的对称轴是取最值的地方，所以两相邻对称轴的距离是半个周期
所以T=π
所以T=2π/π=2
偶函数
f(-x)=2sin(-2x+q-π/6)=f(x)=2sin(2x+q-π/6)
所以-2x+q-π/6=2kπ+2x+q-π/6
或-2x+q-π/6=2kπ+π-(2x+q-π/6)

-2x+q-π/6=2kπ+2x+q-π/6
这个不是恒等式，舍去

-2x+q-π/6=2kπ+π-(2x+q-π/6)
2q=2kπ+4π/3
q=kπ+2π/3
所以q=2π/3

f(x)=2sin(2x+2π/3)
f(π/8)=2sin(π/4+2π/3)=2sinπ/4cos2π/3+2cosπ/4sin2π/3=(√6-√2)/4