Let f(x)=det(cosxsinx0−sinxcosx0001)f(x) = \det \begin{pmatrix} \cos x & \sin x & 0 \\ -\sin x & \cos x & 0 \\ 0 & 0 & 1 \end{pmatrix}f(x)=detcosx−sinx0sinxcosx0001. Which of the following is true for f(x)f(x)f(x)?
f(x)=cos(2x)f(x) = \cos(2x)f(x)=cos(2x)
f(x)=1f(x) = 1f(x)=1 for all xxx
f(x)=sin(2x)f(x) = \sin(2x)f(x)=sin(2x)
f(x)=sec(x)f(x) = \sec(x)f(x)=sec(x)