Let α and β be the roots of the quadratic equation x2 sin θ - x(sin θ cos θ + 1) + cos θ = 0(0 < θ < 45°), and α < β. Then \(\mathop \sum \limits_{n = 0}^\infty \left( {{\alpha ^n} + \frac{{{{( - 1)}^n}}}{{{\beta ^n}}}} \right)\) is equal to:

\(\frac{1}{{1 + {\rm{cos\;}}\theta }} - \frac{1}{{1 - {\rm{sin\;}}\theta }}\)

\(\frac{1}{{1 - {\rm{cos\;}}\theta }} - \frac{1}{{1 + {\rm{sin\;}}\theta }}\)

\(\frac{1}{{1 + {\rm{cos\;}}\theta }} + \frac{1}{{1 - {\rm{sin\;}}\theta }}\)

\(\frac{1}{{1 - {\rm{cos\;}}\theta }} + \frac{1}{{1 + {\rm{sin\;}}\theta }}\)

Let α and β be the roots of the quadratic equation x2 sin θ - x(sin

1.	Let α and β be the roots of the quadratic equation x2 sin θ - x(sin θ cos θ + 1) + cos θ = 0(0 < θ < 45°), and α < β. Then \(\mathop \sum \limits_{n = 0}^\infty \left( {{\alpha ^n} + \frac{{{{( - 1)}^n}}}{{{\beta ^n}}}} \right)\) is equal to:
A.	\(\frac{1}{{1 - {\rm{cos\;}}\theta }} - \frac{1}{{1 + {\rm{sin\;}}\theta }}\)
B.	\(\frac{1}{{1 + {\rm{cos\;}}\theta }} + \frac{1}{{1 - {\rm{sin\;}}\theta }}\)
C.	\(\frac{1}{{1 - {\rm{cos\;}}\theta }} + \frac{1}{{1 + {\rm{sin\;}}\theta }}\)
D.	\(\frac{1}{{1 + {\rm{cos\;}}\theta }} - \frac{1}{{1 - {\rm{sin\;}}\theta }}\)
Answer» D. \(\frac{1}{{1 + {\rm{cos\;}}\theta }} - \frac{1}{{1 - {\rm{sin\;}}\theta }}\)