Which of the following lists all the solutions of in the interval ?

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

Problem

Which of the following lists all the solutions of cos⁡(3θ)=cos⁡θ\cos(3\theta)=\cos\theta in the interval 0≤θ<2π0\le \theta < 2\pi? (a) {0,  π}\{0,\;\pi\} (b) {π2,  π,  3π2}\left\{\dfrac{\pi}{2},\;\pi,\;\dfrac{3\pi}{2}\right\} (c) {0,  π2,  π,  3π2}\{0,\;\dfrac{\pi}{2},\;\pi,\;\dfrac{3\pi}{2}\} (d) {π3,  π,  5π3}\left\{\dfrac{\pi}{3},\;\pi,\;\dfrac{5\pi}{3}\right\}

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