Let \( \lambda \) and \( \alpha \) be real. Let \( S \) denote the ...

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Let \( \lambda \) and \( \alpha \) be real. Let \( S \) denote the set of all values of \( \lambda \) for which the system of linear equations
\( \mathrm{P} \)
\[
\begin{array}{l}
\lambda x+(\sin \alpha) y+(\cos \alpha) z=0 \\
x+(\cos \alpha) y+(\sin \alpha) z=0 \\
-x+(\sin \alpha) y-(\cos \alpha) z=0
\end{array}
\]
W
has a non-trivial solution, then \( S \) contains
(a) \( (-1,1) \)
(b) \( [-\sqrt{2},-1] \)
(c) \( [1, \sqrt{2}] \)
(d) \( (-2,2) \)
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