question_answer

If \[f(x)=\left| \begin{matrix}    {{\sec }^{2}}x & 1 & 1  \\    {{\cos }^{2}}x & {{\cos }^{2}}x & \cos e{{c}^{2}}x  \\    1 & {{\cos }^{2}}x & {{\cot }^{2}}x  \\ \end{matrix} \right|,\] then

A)  \[\int\limits_{-\pi /4}^{\pi /4}{f\,\,(x)\,\,dx=\frac{1}{16}\,\,(3\pi +8)}\]

B)  \[f'\,\,(\pi /2)=0\]

C)  Maximum value of f(x) is 1.

D)  Minimum value of f(x) is 0.

E)  All of these