Diagnostic Tests - D Diagnostic Tests: Trigonometry - Page xxx: 8

$x = 0, ~~\frac{\pi}{3},~~\pi, ~~\frac{5\pi}{3}, ~~2\pi$

$sin~2x = sin~x$ $2~sin~x~cos~x = sin~x$ Case 1: $sin~x = 0$ $x = 0, \pi, 2\pi$ Case 2: $sin~x \neq 0$ $2~sin~x~cos~x = sin~x$ $2~cos~x = 1$ $cos~x = \frac{1}{2}$ $x = \frac{\pi}{3}, \frac{5\pi}{3}$