What is the general solution for 3tan^2(2x)-1=0 ?

The general solution for 3tan^2(2x)-1=0 is x= pi/(12)+(pin)/2 ,x=-pi/(12)+(pin)/2

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

3 tan^{2} (2 x) - 1 = 0

x = \frac{π}{12} + \frac{πn}{2}, x = - \frac{π}{12} + \frac{πn}{2}

Solution steps

3 tan^{2} (2 x) - 1 = 0

Solve by substitution

tan (2 x) = \frac{1}{3}, tan (2 x) = - \frac{1}{3}

tan (2 x) = \frac{1}{3} : x = \frac{π}{12} + \frac{πn}{2}

tan (2 x) = - \frac{1}{3} : x = - \frac{π}{12} + \frac{πn}{2}

Combine all the solutions

x = \frac{π}{12} + \frac{πn}{2}, x = - \frac{π}{12} + \frac{πn}{2}

cos (θ) = - \frac{1}{4}

sin (2 x) = 2 cos^{2} (x)

cos (x) = 3

sin (2 θ) = 3 cos (θ)

cos (θ) = - \frac{2}{5}

What is the general solution for 3tan^2(2x)-1=0 ?
The general solution for 3tan^2(2x)-1=0 is x= pi/(12)+(pin)/2 ,x=-pi/(12)+(pin)/2