How do you solve for x in 3sin2x=cos2x for the interval 0 ≤ x < 2π

1 Answer
Feb 13, 2015

You can use the fact that tan(x)=sin(x)/cos(x)
In your expression.:
3*sin(2x)=cos(2x)
3*sin(2x)/cos(2x)=1 and
tan(2x)=1/3
tan(2x) is equal to 1/3 for 2x=0.321 and 3.463 rad in your interval;

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(Graph from: http://www.intmath.com/trigonometric-graphs/4-graphs-tangent-cotangent-secant-cosecant.php)

and so to have x you divide by 2 to get: x=0.160 and 1.731 rad

Hope it helps