If satisfies the equation

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

If exp⁡[(sin⁡2x+sin⁡4x+sin⁡6x+⋯ )ln⁡2]\exp\left[\left(\sin^2x+\sin^4x+\sin^6x+\cdots\right)\ln2\right] satisfies the equation y2−9y+8=0y^2-9y+8=0, then the value of cos⁡xcos⁡x+sin⁡x\frac{\cos x}{\cos x+\sin x}, where 0<x<π20<x<\frac{\pi}{2}, is (1) 3+1\sqrt3+1 (2) 3−12\frac{\sqrt3-1}{2} (3) 3−1\sqrt3-1 (4) None of these

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