Mathematics - Quadratic Equation Question with Solution | TestHub

Let$E=\frac{{\alpha }^{12}+{\beta }^{12}}{\left({\alpha }^{-12}+{\beta }^{-12}\right){\left(\alpha -\beta \right)}^{24}}=\frac{{\alpha }^{12}+{\beta }^{12}}{\frac{{\alpha }^{12}+{\beta }^{12}}{{\alpha }^{12}\times {\beta }^{12}}{\left(\alpha -\beta \right)}^{24}}$
$E=\frac{{\left(\alpha \beta \right)}^{12}}{{\left(\alpha -\beta \right)}^{24}}=\frac{{\left(\alpha \beta \right)}^{12}}{{\left[{\left(\alpha +\beta \right)}^2-4\alpha \beta \right]}^{12}}$
Now$\alpha +\beta =-sin\theta$
$\alpha \beta =-2sin\theta$
$\therefore E=\frac{{\left(-2sin\theta \right)}^{12}}{{\left[{\left(-sin\theta \right)}^2-4\left(-2sin\theta \right)\right]}^{12}}$
$=\frac{2^{12}}{{\left(8+sin\theta \right)}^{12}}$