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 = (\pi)/(2) + k\pi \\ \sin(x) = (1)/(2) > > > x = (\pi)/(6) + 2k\pi \\ or \: x = (5\pi)/(6) + 2k\pi`

`x = (\pi)/(2) or (3\pi)/(2) \\ x = (\pi)/(6) or (5\pi)/(6)`