Let \( \alpha, \beta, \gamma, a, b, c, x \in \mathbf{R} \) and let
...
Let \( \alpha, \beta, \gamma, a, b, c, x \in \mathbf{R} \) and let
\[
\Delta=\left|\begin{array}{lll}
\sin (x+\alpha) & \cos (x+\alpha) & a+x \sin \alpha \\
\sin (x+\beta) & \cos (x+\beta) & b+x \sin \beta \\
\sin (x+\gamma) & \cos (x+\gamma) & c+x \sin \gamma
\end{array}\right|
\]
then \( \Delta \) is
(a) independent of \( x \)
(b) dependent of \( \alpha, \beta, \gamma \)
(c) dependent on \( a, b, c \)
(d) a constant
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