Question

Find all solutions in the interval [0, 2π) sin2x + sin x = 0

Answer 1

Sin 2 x + sin x = 0
( sin 2 x = 2 sin x cos x )
2 sin x cos x + sin x  = 0
sin x ( 2 cos x + 1 ) = 0
sin x = 0 
x 1 = 0
x 2 = π 
or: 2 cos x + 1 = 0
2 cos x = - 1
cos x = -1/2
x 3 = 2π/3
x 4 = 4π/3