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

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

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\qquad\text{(i)} sin⁡2x−cos⁡2x=2−sin⁡2x(ii)\sin^2x-\cos2x=2-\sin2x\qquad\text{(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 (1) −1-1 (2) −53+213-\frac{5}{3}+\frac{2}{\sqrt{13}} (3) 53−213\frac{5}{3}-\frac{2}{\sqrt{13}} (4) 53+213\frac{5}{3}+\frac{2}{\sqrt{13}}

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