Question

Find all solutions to the equation sin2x + sin x = 0, sin2x = -sinx hint: sin2x = 2sinxcosx

Answer 1

Sin 2 x + sin x = 0,
2 sin x cos x + sin x = 0
sin x ( 2 cos x + 1 ) = 0
sin x = 0                 or :     2 cos x + 1 = 0
x 1 = k π                          2 cos x = - 1
k ∈ Z                                cos x = - 1/2
                                         x 2 = 2π/3 + 2 kπ,  x 3 = 4π/3 + 2 kπ,  k ∈ Z