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

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

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3tan^2(2x)=1

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

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

Solution steps

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

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}

tan (x) + cot (x) = 3

3 sin (B) - 2 = 5 sin (B) - 1

sin (x) = sin (- x)

3 cos (θ) + 2 = 0

- cot (x) - 3 cos (x) = - cot (x) cos (x) - 3 cos (x)

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