If \( f(x)=\left|\begin{array}{ccc}\sec x & \cos x & \sec ^{2} x+\operatorname{cosec} x \cot x \...
If \( f(x)=\left|\begin{array}{ccc}\sec x & \cos x & \sec ^{2} x+\operatorname{cosec} x \cot x \\ \cos ^{2} x & \cos ^{2} x & \operatorname{cosec}^{2} x \\ 1 & \cos ^{2} x & \cos ^{2} x\end{array}\right| \) then, \( \int_{0}^{\pi / 2} f(x) d x \) equals
(A) 0
(B) 1
(C) \( -\left(\frac{\pi}{4}+\frac{8}{15}\right) \)
(D) \( -1 \)
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