Given that
\[
\begin{aligned}
f(\alpha) &=\left|\begin{array}{ccc}
\cos (x+\alpha) & -\sin (x+\a...
Given that
\[
\begin{aligned}
f(\alpha) &=\left|\begin{array}{ccc}
\cos (x+\alpha) & -\sin (x+\alpha) & \cos 2 \alpha \\
\sin x & \cos x & \sin \alpha \\
-\cos x & \sin x & \cos \alpha
\end{array}\right| \\
&=A+B \cos 2 \alpha
\end{aligned}
\]
then
(a) \( A=0, B=1 \)
(b) \( A=1, B=1 \)
(c) \( A=1, B=0 \)
(d) \( A=1, B=-1 \)
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