Solve 3tan^2 x-1=0 for all solutions [0, 2pi]?

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Solve 3tan^2 x-1=0 for all solutions [0, 2pi]?

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Answer 1 · 2016-10-17T06:36:25

$x in {pi/6, (5pi)/6, (7pi)/6, (11pi)/6}$

Explanation:

$3tan^2(x) - 1 = 0$

$=> tan^2(x) = 1/3$

$=> tan(x) = +-1/sqrt(3)$

Finding what values for $n$ put these within the interval $[0, 2pi)$ , we get $n in {0, 1}$ for $x=pi/6+npi$ and $n in {1, 2}$ for $x = -pi/6+npi$ . Thus, our total solution set is

$x in {pi/6, (5pi)/6, (7pi)/6, (11pi)/6}$

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Solve 3tan^2 x-1=0 for all solutions [0, 2pi]?

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