A simple formula may help you out
cos(2x) = cos^2(x) - sin^2(x)
= - { sin^2(x) -cos^2(x) }
= - f(x)
Therefore f(x) = -cos(2x)
So f( π/6) = - cos (2*π/6) = -cos(π/3) = -1/2
If f(x)=1+cos2x+8sin2xsin 2x. Then the minimum value of f(x) is