What is the general solution for 2tan^2(3x)=6 ?

The general solution for 2tan^2(3x)=6 is x= pi/9+(pin)/3 ,x=(2pi)/9+(pin)/3

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2tan^2(3x)=6

2 tan^{2} (3 x) = 6

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

Solution steps

2 tan^{2} (3 x) = 6

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}

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

sinh (x) = \frac{- 3}{4}

1 - cos (θ) = cos (θ)

(cos (x) - 5) (cos (x) + 1) = 0

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

What is the general solution for 2tan^2(3x)=6 ?
The general solution for 2tan^2(3x)=6 is x= pi/9+(pin)/3 ,x=(2pi)/9+(pin)/3