The equation is to be solved for

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

Problem

The equation sin⁡3x=sin⁡x\sin 3x=\sin x is to be solved for 0≤x<2π0\le x<2\pi. Which of the following set contains all the solutions? (a) x=0, π4, 3π4, π, 5π4, 7π4, 2πx=0,\,\dfrac{\pi}{4},\,\dfrac{3\pi}{4},\,\pi,\,\dfrac{5\pi}{4},\,\dfrac{7\pi}{4},\,2\pi (b) x=0, π2, π, 3π2x=0,\,\dfrac{\pi}{2},\,\pi,\,\dfrac{3\pi}{2} (c) x=0, π4, 3π4, π, 5π4, 7π4x=0,\,\dfrac{\pi}{4},\,\dfrac{3\pi}{4},\,\pi,\,\dfrac{5\pi}{4},\,\dfrac{7\pi}{4} (d) x=π4, 3π4, π, 5π4, 7π4x=\dfrac{\pi}{4},\,\dfrac{3\pi}{4},\,\pi,\,\dfrac{5\pi}{4},\,\dfrac{7\pi}{4}

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