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^(o)), and α < β. Then Σ n = 0 ^∞ (α ⁿ + ((- 1)ⁿ)/(β ⁿ)) is equal to:

(B) 1/(1 - cos θ) + 1/(1 + sin θ)

(A) 1/(1 + cos θ) + 1/(1 - sin θ)

(C) 1/(1 - cos θ) - 1/(1 + sin θ)

(D) 1/(1 + cos θ) - 1/(1 - sin θ)

Complex Numbers and Quadratic Equations: JEE Main 2019 Mathematics question

JEE Main 2019 · 11 Jan, Evening shift · Q5134

JEE Main 201911 Jan, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha

and

\beta

be the roots of the quadratic equation x² sin

\theta

– x(sin

\theta

cos

\theta

+ 1) + cos

\theta

= 0 (0 <

\theta

< 45^o), and

\alpha

\beta

. Then

\sum\limits_{n = 0}^\infty {\left( {{\alpha ^n} + {{{{\left( { - 1} \right)}^n}} \over {{\beta ^n}}}} \right)}

is equal to :