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

Question

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

Answer 1

 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