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The equation of a line which passes through \( \left(a \cos ^{3} \theta, a \sin ^{3} \theta\right) \) and perpendicular to the line \( x \sec \theta+y \operatorname{cosec} \theta=a \), is
(A) \( x \cos \theta+y \sin \theta=2 a \cos 2 \theta \)
(B) \( x \sin \theta-y \cos \theta=2 a \sin 2 \theta \)
(C) \( x \sin \theta+y \cos \theta=2 a \cos 2 \theta \)
(D) none of these
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