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The equation to the straight line passing through the point \[(a{{\cos }^{3}}\theta ,\ a{{\sin }^{3}}\theta )\] and perpendicular to the line \[x\sec \theta +y\,\text{cosec}\,\theta =a,\] is                                                                 [AMU 1975]

A)            \[x\cos \theta -y\sin \theta =a\cos \ 2\theta \]

B)            \[x\cos \theta +y\sin \theta =a\cos \ 2\theta \]

C)            \[x\sin \theta +y\cos \theta =a\cos \ 2\theta \]                           

D)            None of these