Solve the equation in the interval by answering the following

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve the equation sin⁡x=sin⁡2x\sin x=\sin 2x in the interval 0<x<2π0< x<2\pi by answering the following. (i) Show that sin⁡x−sin⁡2x=2cos⁡(3x2)sin⁡(−x2)\sin x-\sin 2x=2\cos\left(\dfrac{3x}{2}\right)\sin\left(-\dfrac{x}{2}\right). (ii) Hence obtain all the values of xx satisfying sin⁡x=sin⁡2x\sin x=\sin 2x in 0<x<2π0< x<2\pi. (iii) How many distinct solutions does the equation possess in the given interval?

Related theory

Browse the problem library