If tanθ = a/b, find the value of \(\frac{{{\rm{a}}\sin {\rm{\theta }} - {\rm{b}}\cos {\rm{\theta }}}}{{{\rm{a}}\sin {\rm{\theta \;}} + {\rm{\;b}}\cos {\rm{\theta }}}}\)
1
\(\frac{{{{\rm{a}}^2} - {{\rm{b}}^2}}}{{{{\rm{a}}^2}{\rm{\;}} + {\rm{\;}}{{\rm{b}}^2}}}\)
2
\(\frac{{{{\rm{b}}^2} - {{\rm{a}}^2}}}{{{{\rm{a}}^2}{\rm{\;}} + {\rm{\;}}{{\rm{b}}^2}}}\)
3
\(\frac{{{{\rm{a}}^2}{\rm{\;}} + {\rm{\;}}{{\rm{b}}^2}}}{{{{\rm{a}}^2} - {{\rm{b}}^2}}}\)
4
None of these