Let [tex]\sf \alpha[/tex] and [tex]\sf \beta[/tex] be the roots of quadratic equation, x²sin∅ - x(sin∅cos∅ + 1) + cos∅ = 0 where ∅ [tex]\epsilon[/tex] (0,45) and [tex]\alpha < \beta[/tex] . Find the value of :
[tex]\sf {}^{ \infty } \sum_{{n = 0}} \bigg( { \alpha }^{n} + \dfrac{( - 1) {}^{n} }{ \beta {}^{n} } \bigg)[/tex]
[tex]\sf {}^{ \infty } \sum_{{n = 0}} \bigg( { \alpha }^{n} + \dfrac{( - 1) {}^{n} }{ \beta {}^{n} } \bigg)[/tex]
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