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 α\alpha is a root of (i) and β\beta is a root of (ii), then tan⁡α+tan⁡β\tan \alpha + \tan \beta can be equal to a. 1+69/61 + \sqrt{69}/6 b. −1−69/6-1 - \sqrt{69}/6 c. −3+696\frac{-3 + \sqrt{69}}{6} d. 3−693\frac{3 - \sqrt{69}}{3}

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