If \(\left( {\frac{{{\rm{tan\theta }} - {\rm{sec\theta \;}} + {\rm{\;}}1}}{{{\rm{tan\theta \;}} + {\rm{\;sec\theta }} - 1}}} \right){\rm{sec\theta \;}} = {\rm{\;}}\frac{1}{{\rm{k}}}\) then k = ?

• A. 1 – sinθ
• B. 1 + cosθ
• C. 1 + sinθ
• D. 1 – cosθ