If \( \sqrt{2} \cos A=\cos B+\cos ^{3} B \) and \( \sqrt{2} \sin A=\sin B-\sin ^{3} B \), then t...
If \( \sqrt{2} \cos A=\cos B+\cos ^{3} B \) and \( \sqrt{2} \sin A=\sin B-\sin ^{3} B \), then the possible value of \( \sin (A-B) \) is/are
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( -\frac{1}{2} \)
(d) \( -\frac{1}{3} \)
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