What are all the exact solutions of 2sin^2x-sinx=0 for 0

x = {0, π/6}

Step-by-step explanation:

2sin^2x-sinx=0

and i know the answer is this ...

2sin² (x) - sin (x) = 0

sin2 (x) is sin (x) * sin (x) so 2sin² (x) - sin (x) = 2 sin (x) * sin (x) - sin (x) and this expression has a common factor of sin (x) so

2sin² (x) - sin (x) = 2 sin (x) * sin (x) - sin (x) = sin (x) [2 sin (x) - 1]

sin (x) (2sin (x) - 1) = 0

sin (x) = 0

x = 0

2sin (x) - 1 = 0

sin (x) = 1/2

x = π/6

x = {0, π/6}