Let and be real numbers such that

MATHEMATICS · Subjective · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

Let α\alpha and β\beta be real numbers such that −π4<β<0<α<π4-\frac{\pi}{4} < \beta < 0 < \alpha < \frac{\pi}{4}. If sin⁡(α+β)=13\sin(\alpha + \beta) = \frac{1}{3} and cos⁡(α−β)=23\cos(\alpha - \beta) = \frac{2}{3}, then the greatest integer less than or equal to (sin⁡αcos⁡β+cos⁡βsin⁡α+cos⁡αsin⁡β+sin⁡βcos⁡α)2\left( \frac{\sin \alpha}{\cos \beta} + \frac{\cos \beta}{\sin \alpha} + \frac{\cos \alpha}{\sin \beta} + \frac{\sin \beta}{\cos \alpha} \right)^2 is _____ .

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