sin 2x+sinx=0

Question

find all real numbers in the interval (0, 2 pi) that satisfy the equation

Answer 1

Since

sin 2x = 2 sin x cosx

 

Substitute:

2 sin x cos x + sinx = 0

 

Factor out sin x:

 

sin x(2 cos x + 1) = 0

 

sin x = 0           2 cos x = -1

 

x = 0, pi            cos x = -1/2

                      

                        x = 2pi/3, 4pi/3

 

 

 

x = 0, 2pi/3, pi, 4pi/3