If sin x + sin y = a and cos x + cos y = b, then \({\tan ^2}\left( {\frac{{{\rm{x}} + {\rm{y}}}}{2}} \right) + {\tan ^2}\left( {\frac{{{\rm{x}} - {\rm{y}}}}{2}} \right)\) is equal to
1
\(\frac{{{{\rm{a}}^4} + {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}\)
2
\(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}\)
3
\(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{a}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{a}}^4}}}\)
4
None of the above