Let the solution set of the equations \[ \sec x+\tan x=\sqrt{3} \] \( 1+\sin x=\sqrt{3} \cos x \...

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Let the solution set of the equations
\[
\sec x+\tan x=\sqrt{3}
\]
\( 1+\sin x=\sqrt{3} \cos x \)
\( \sec 4 x+\sec 2 x=2 \)
\( \cos 2 x+\cos 4 x=2 \cos 2 x \cos 4 x \)
in \( [0,2 \pi] \) be \( S_{1}, S_{2}, S_{3}, S_{4} \) respectively. Then
(a) \( S_{1}=S_{2} \)
(b) \( S_{1} \subset S_{2} \)
(c) \( S_{3}=S_{4} \)
(d) \( S_{3} \subset S_{4} \)
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