Consider the equations 5 ^2x+3 x x-3 ^2x=2

MATHEMATICS · Single correct · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Consider the equations 5sin⁡2x+3sin⁡xcos⁡x−3cos⁡2x=2…(i)5\sin^2x+3\sin x\cos x-3\cos^2x=2\quad\dots\text{(i)} sin⁡2x−cos⁡2x=2−sin⁡2x…(ii)\sin^2x-\cos2x=2-\sin2x\quad\dots\text{(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 (1) 1+6961+\frac{\sqrt{69}}{6} (2) −1−696-1-\frac{\sqrt{69}}{6} (3) −3+696\frac{-3+\sqrt{69}}{6} (4) 3−693\frac{3-\sqrt{69}}{3}

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