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

The general solution for tan^2(3x)=3 is x= pi/9+(pin)/3 ,x=(2pi)/9+(pin)/3

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tan^2(3x)=3

tan^{2} (3 x) = 3

x = \frac{π}{9} + \frac{πn}{3}, x = \frac{2 π}{9} + \frac{πn}{3}

Solution steps

tan^{2} (3 x) = 3

Solve by substitution

tan (3 x) = 3, tan (3 x) = - 3

tan (3 x) = 3 : x = \frac{π}{9} + \frac{πn}{3}

tan (3 x) = - 3 : x = \frac{2 π}{9} + \frac{πn}{3}

Combine all the solutions

x = \frac{π}{9} + \frac{πn}{3}, x = \frac{2 π}{9} + \frac{πn}{3}

cos (x) - 3 sin (x) = 2

tan (x) = - 3

sec (θ) = - 2

tan^{2} (θ) = \frac{3}{2} sec (θ)

cot^{2} (x) - 3 = 0

What is the general solution for tan^2(3x)=3 ?
The general solution for tan^2(3x)=3 is x= pi/9+(pin)/3 ,x=(2pi)/9+(pin)/3