question_answer

Passage (Q. - 89) Let \[{{S}_{1}}\] be the set of all those solutions of the equation\[(1+a)cos\theta cos(2\theta -b)=\]\[(1+acos2\theta )cos(\theta -b)\]which are independent of a and b and \[{{S}_{2}}\] be the set of all such solutions which are dependent on a and b. Then Conditions that should be imposed on a and b such that \[{{S}_{2}}\] is non-empty.

A) \[\left| \frac{a}{2}\sin b \right|<1\]                       

B) \[\left| \frac{a}{2}\sin b \right|\le 1\]

C) \[|a\sin b|\le 1\]                            

D)  None of these