Solve the equation 3sin(2x)+3sinx=0 on the interval 0 ≤ pi <2pi. Give the sum of all the solutions.

Answer 1

sin 2x = 2 sin x cos c
so
6 sin x cos x + 3 sin x = 0
6 cos x + 3 = 0
cos x = - 1/2
cos is negative in quadrants 2 and 3
so pi/2 < x < 3 pi/2
180 - 60 degrees and 180 + 60 degrees
is
pi - pi/3 and pi + pi/3
2 pi/3 and 4 pi/3

Answer 2

don't forget the solutions at sinx = 0