Question

Find all values of x in the interval [0,2π] that satisfy the equation sin2x=cosx. enter your answers as a list of numbers separated by commas,
e.g. '1,pi/3,4'.

Answer 1

$\sin(2x) = \cos(x) \\ 2 \sin(x) \cos(x) = \cos(x) \\ \cos(x) (2 \sin(x) - 1) = 0$
so
$\cos(x) = 0 > > > x = \frac{\pi}{2} + k\pi \\ \sin(x) = \frac{1}{2} > > > x = \frac{\pi}{6} + 2k\pi \\ or \: x = \frac{5\pi}{6} + 2k\pi$
$x = \frac{\pi}{2} or \frac{3\pi}{2} \\ x = \frac{\pi}{6} or \frac{5\pi}{6}$