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

The general solution for tan^2(3x)=1 is x= pi/(12)+(pin)/3 ,x= pi/4+(pin)/3

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tan^2(3x)=1

tan^{2} (3 x) = 1

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

Solution steps

tan^{2} (3 x) = 1

Solve by substitution

tan (3 x) = 1, tan (3 x) = - 1

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

tan (3 x) = - 1 : x = \frac{π}{4} + \frac{πn}{3}

Combine all the solutions

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

3 + 3 sin (θ) = 0

cos (2 x) = \frac{( 8 k - 7 )}{7}

cos^{2} (x) - 3 sin (2 x) + sin^{2} (x) + 2 sin^{2} (2 x) = 0

2 cos^{2} (x) + sin (- x) - 1 = 0

cos (x) = \frac{- 1}{4}

What is the general solution for tan^2(3x)=1 ?
The general solution for tan^2(3x)=1 is x= pi/(12)+(pin)/3 ,x= pi/4+(pin)/3