# Answer to Question #25332 in Trigonometry for bunga

Question #25332

solve this.

3 sin 2x = 2 sin x

3 sin 2x = 2 sin x

Expert's answer

3 sin 2x = 2 sin xLet's expand sin2x:

3*2sin(x)cos(x)-2sin(x)=0Now we factor out common multiplier:

2sin(x)* ( 3cos(x)-1)=0

so sin(x)=0 or cos(x)=1/3Thus, the solutions in general form are

x=pi*k where k integer

or x=2*pi*n+cos^-1(1/3)

or x=2*pi*n-cos^-1(1/3), where n integer

3*2sin(x)cos(x)-2sin(x)=0Now we factor out common multiplier:

2sin(x)* ( 3cos(x)-1)=0

so sin(x)=0 or cos(x)=1/3Thus, the solutions in general form are

x=pi*k where k integer

or x=2*pi*n+cos^-1(1/3)

or x=2*pi*n-cos^-1(1/3), where n integer

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