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Official 2016 Paper 1 · Q17

Paper 1Trigonometry

It is given that

y=(1+2cos⁡x)cos⁡2xfor 0<x<πy=(1+2\cos x)\cos2x\quad\text{for }0<x<\pi

The complete set of values of xx for which yy is negative is

A0<x<π4,2π3<x<3π40<x<\dfrac{\pi}{4},\quad\dfrac{2\pi}{3}<x<\dfrac{3\pi}{4}
B0<x<π4,3π4<x<π0<x<\dfrac{\pi}{4},\quad\dfrac{3\pi}{4}<x<\pi
C0<x<2π3,3π4<x<π0<x<\dfrac{2\pi}{3},\quad\dfrac{3\pi}{4}<x<\pi
Dπ4<x<2π3,3π4<x<π\dfrac{\pi}{4}<x<\dfrac{2\pi}{3},\quad\dfrac{3\pi}{4}<x<\pi
Eπ4<x<2π3\dfrac{\pi}{4}<x<\dfrac{2\pi}{3}
Fπ4<x<3π4\dfrac{\pi}{4}<x<\dfrac{3\pi}{4}

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