Let be such that 2 (1- )= ^2 ( 2 + 2 ) -1,

MATHEMATICS · Multi correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let θ,ϕ∈[0,2π]\theta,\phi\in[0,2\pi] be such that 2cos⁡θ(1−sin⁡ϕ)=sin⁡2θ(tan⁡θ2+cot⁡θ2)cos⁡ϕ−1,2\cos\theta(1-\sin\phi)=\sin^2\theta\left(\tan\frac{\theta}{2}+\cot\frac{\theta}{2}\right)\cos\phi-1, tan⁡(2π−θ)>0\tan(2\pi-\theta)>0, and −1<sin⁡θ<−32-1<\sin\theta<-\frac{\sqrt{3}}{2}. Then ϕ\phi cannot satisfy (1) 0<ϕ<π20<\phi<\frac{\pi}{2} (2) π2<ϕ<4π3\frac{\pi}{2}<\phi<\frac{4\pi}{3} (3) 4π3<ϕ<3π2\frac{4\pi}{3}<\phi<\frac{3\pi}{2} (4) 3π2<ϕ<2π\frac{3\pi}{2}<\phi<2\pi

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