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Find all solutions to the equation in the interval [0, 2π). (3 points) sin 2x - sin 4x = 0

pi divided by six , pi divided by two , five pi divided by six , seven pi divided by six , three pi divided by two , eleven pi divided by six

0, pi divided by six , pi divided by two , five pi divided by six , π, seven pi divided by six , three pi divided by two , eleven pi divided by six

0, two pi divided by three , four pi divided by three

0, pi divided by three. , two pi divided by three. , π, four pi divided by three. , five pi divided by three.

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ghanami

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello :

in the interval [0, 2π).  sin 2x - sin 4x = 0   means :

sin 2x =sin 4x

all solutions in R :4x=2x+2kπ   or  4x = π -2x +2k'π    k , k'  in Z

2x = 2kπ or 6x= (2k'+1)π

x = kπ  or x = (2k'+1)π/6

in :  [0, 2π)     k =0   k =1    so : x=0   x=π

k' = 0  ,  k' =1 ,   k' = 2    , k'=3  , k'= 4   , k' = 5  

so x= π/6     x= π/2   x= 7π/6    x= 3π/2    x= 11π/6

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