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Find all solutions in the interval [0,2pi): sin2x=cosx

This is for my trig class, thanks for the help! If you could, could you please show all your work? Thanks again!

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
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 Sin 2X = CosX
 
  2 Sinx CosX - CosX =0
 
    CosX ( 2 Sin X - 1 ) =0
 
   Cos X = 0      X = 90° = π/2     or X = 270° = 3π/4
 
 
     2SinX = 1       X = 30° = π/6  or  X = 150° = 5π/6