A hyperbola, having the transverse axis of length \(2 \sin \theta\) is confocal with the ellipse \(3 x^{2}+4 y^{2}=12\). Its equation is
(A) \(x^{2} \sin ^{2} \theta-y^{2} \cos ^{2} \theta=1\)
(B)
\(x^{2} \operatorname{cosec}^{2} \theta-y^{2} \sec ^{2} \theta=1\)
(C) \(\left(x^{2}+y^{2}\right) \sin ^{2} \theta=1+y^{2}\)
(D)
\(x^{2} \operatorname{cosec}^{2} \theta=x^{2}+y^{2}+\sin ^{2} \theta\)