question_answer

If \[\sin (\theta +\alpha )=a\] and \[\sin (\theta +\beta )=b,\] then \[\cos \,2\,\,(\alpha -\beta )-4\,ab\cos \,\,(\alpha -\beta )\] is equal to

A)  \[2+{{a}^{2}}+{{b}^{2}}\]            

B)  \[2-{{a}^{2}}-{{b}^{2}}\]

C)  \[1-2{{a}^{2}}-2{{b}^{2}}\]

D)  \[1+2{{a}^{2}}+2{{b}^{2}}\]

E)  None of these