Let is a root of the equation

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let α\alpha is a root of the equation (2sin⁡x−cos⁡x)(1+cos⁡x)=sin⁡2x(2 \sin x - \cos x)(1 + \cos x) = \sin^2 x , β\beta is a root of the equation 3cos⁡2x−10cos⁡x+3=03 \cos^2 x - 10 \cos x + 3 = 0 and γ\gamma is a root of the equation 1−sin⁡2x=cos⁡x−sin⁡x1 - \sin 2x = \cos x - \sin x , 0≤α,β,γ≤π20 \le \alpha, \beta, \gamma \le \frac{\pi}{2} . cos⁡α+cos⁡β+cos⁡γ\cos \alpha + \cos \beta + \cos \gamma can be equal to (1) 36+22+662\frac{3\sqrt{6} + 2\sqrt{2} + 6}{6\sqrt{2}} (2) 33+86\frac{3\sqrt{3} + 8}{6} (3) 33+26\frac{3\sqrt{3} + 2}{6} (4) None of these

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