Question

find the general solution of equation sin 2x + sin 4x + sin 6x =0

Answer 1

the equation can be written as sin6x +sin2x + sin4x =0
2sin4x cos2x +sin4x =0
sin4x(2cos2x-1) =0
therefore sin4x=0 or cos 2x =1 divided by 2
sin4x =0 or cos2x=cos pieby 3
hence general sol. can be written as 4x=npie or 2npie+- pie by 3.

Answer 2

Sin2x+sin 6x+sin 4x
2 sin 4x cos2x+sin 4x=0
Sin 4x(2cos2x+1)=0
Sin 4x=0 or 2cos2x+1=0
4x =n(pi) then x=n(pi) /4
2Cos 2x+1 =0
2Cos 2x=-1 then cos 2x=-1/2
2x=2n(pi)+ or - ( 2pi/3)
X=n(pi) +or-( pi)/3