Let \( 0\theta\pi / 2 \) and
\[
\Delta(x, \theta)=\left|\begin{arra...
Let \( 0\theta\pi / 2 \) and
\[
\Delta(x, \theta)=\left|\begin{array}{ccc}
x & \tan \theta & \cot \theta \\
-\tan \theta & -x & 1 \\
\cot \theta & 1 & x
\end{array}\right|
\]
then
(a) \( \Delta(0, \theta)=0 \)
(b) \( \Delta(x, \pi / 4)=-x^{3}+x \)
(c) \( \operatorname{Min}_{0\theta\pi / 2} \Delta(1, \theta)=0 \)
(d) \( \Delta(x, \theta) \) is independent of \( x \)
E
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