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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'.

User Rimer
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1 Answer

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\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)
User GLee
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