Đáp án đúng: A
Giải chi tiết:\(\eqalign{ & B = {(\cos a + \sin b)^2} + {(\sin a - \cos b)^2} = {\cos ^2}a + 2\cos a\sin b + {\sin ^2}b + {\sin ^2}a - 2\sin a\cos b + {\cos ^2}b \cr & = \left( {{{\cos }^2}a + {{\sin }^2}a} \right) + \left( {{{\sin }^2}b + {{\cos }^2}b} \right) - 2(\sin a\cos b - \cos a\sin b) \cr & = \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2\sin \left( {a - b} \right) \cr & = 2 - 2\sin {{2\pi } \over 3} = 2 - 2.{{\sqrt 3 } \over 2} = 2 - \sqrt 3 \cr} \)
Chọn: A.