question_answer

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

A)  \[1-2{{a}^{^{2}}}+2{{b}^{2}}\]

B)  \[1+2{{a}^{2}}+2{{b}^{2}}\]

C)  \[1-2{{a}^{2}}-2{{b}^{2}}\]

D)  \[1-2{{a}^{2}}+{{b}^{2}}\]