Question

）已知函数y=sin2x+acos2x的图像关于直线x=π/6对称,则实数a的值为?

Answer 1

f(x)=sin2x+acos2x关于直线x=-π/6对称

且,x属于R

所以f(-π/6-π/6)=f(-π/6+π/6)

f(-π/3)=f(0)

f(-π/3)=sin(-2π/3)+acos(-2π/3)=-(根号3)/2-a/2

f(0)=sin(0)+acos(0)=a

a=-(根号3)/2-a/2

a=-(根号3)/3