Problem

Problem

Consider the equations 5sin⁡2x+3sin⁡xcos⁡x−3cos⁡2x=2…(i)5\sin^2 x + 3\sin x \cos x - 3\cos^2 x = 2 \quad \dots(i) sin⁡2x−cos⁡2x=2−sin⁡2x…(ii)\sin^2 x - \cos 2x = 2 - \sin 2x \quad \dots(ii) If tan⁡α,tan⁡β\tan \alpha, \tan \beta satisfy (i) and cos⁡γ,cos⁡δ\cos \gamma, \cos \delta satisfy (ii), then tan⁡α⋅tan⁡β+cos⁡γ+cos⁡δ\tan \alpha \cdot \tan \beta + \cos \gamma + \cos \delta can be equal to a. -1 b. −53+213-\frac{5}{3} + \frac{2}{\sqrt{13}} c. 53−213\frac{5}{3} - \frac{2}{\sqrt{13}} d. 53+213\frac{5}{3} + \frac{2}{\sqrt{13}}

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