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

The general solution for 3tan^2(3x)=1 is x= pi/(18)+(pin)/3 ,x=-pi/(18)+(pin)/3

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3tan^2(3x)=1

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

x = \frac{π}{18} + \frac{πn}{3}, x = - \frac{π}{18} + \frac{πn}{3}

Solution steps

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

Solve by substitution

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

tan (3 x) = \frac{1}{3} : x = \frac{π}{18} + \frac{πn}{3}

tan (3 x) = - \frac{1}{3} : x = - \frac{π}{18} + \frac{πn}{3}

Combine all the solutions

x = \frac{π}{18} + \frac{πn}{3}, x = - \frac{π}{18} + \frac{πn}{3}

- 2 (cos (2 x) + sin (x)) = 0

cos (x) + cos^{2} (x) = 1

6 tan (x) - 5 csc (x) = 0

2 (19) tan (\frac{θ}{2}) = 6.3

3 csc (x) - 6 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

What is the general solution for 3tan^2(3x)=1 ?
The general solution for 3tan^2(3x)=1 is x= pi/(18)+(pin)/3 ,x=-pi/(18)+(pin)/3