Let \[ f(x)=\left|\begin{array}{ccc} 1 & \cos x & 1-\cos x \\ 1+\si...

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Let
\[
f(x)=\left|\begin{array}{ccc}
1 & \cos x & 1-\cos x \\
1+\sin x & \cos x & 1+\sin x-\cos x \\
\sin x & \sin x & 1
\end{array}\right|
\]
then
(a) minimum value of \( f(x) \) is \( -1 / 2 \)
(b) maximum value of \( f(x) \) is \( 1 / 2 \)
(c) \( \int_{0}^{\pi / 2} f(x) d x=-1 / 2 \)
(d) maximum value of \( 1+2 f(x) \) is 2
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