SOLUTION: Give the general solution to the equation sinx+sin2x+sin3x=0

sin(x) + sin(2x) + sin(3x) = 0.     (1)


Apply the trigonometry formula   = 

     (see any serious textbook in trigonometry or the lessons 

         - FORMULAS FOR TRIGONOMETRIC FUNCTIONS
         - Addition and subtraction of trigonometric functions

      in this site) to the first and third addend in the left side of the original equation (1).   You will get

 =  =  = .

Now, the equation (1) takes the form

 = ,   or

 = .

This equation deploys in two independent equations


1.  sin(2x) = 0  --->  x = , x = ,  k = 0, =/-1, +/-2. . . . 


2.  2cos(x) + 1 = 0  --->  cos(x) =   --->  x = ,  x = ,  k = 0, =/-1, +/-2. . . . 


Answer.  The solutions are  a)  x = , x = ,  k = 0, =/-1, +/-2. . . .    and 

                            b)  x = ,  x = ,  k = 0, =/-1, +/-2. . . . 





Plot y = sin(x) + sin(2x) + sin(3x)