What is the general solution for 3sqrt(3)+2tan(x)=2sqrt(3)-tan(x) ?

The general solution for 3sqrt(3)+2tan(x)=2sqrt(3)-tan(x) is x=(5pi)/6+pin

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3sqrt(3)+2tan(x)=2sqrt(3)-tan(x)

33 + 2 tan (x) = 23 - tan (x)

x = \frac{5 π}{6} + πn

Solution steps

33 + 2 tan (x) = 23 - tan (x)

Solve by substitution

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

tan (x) = - \frac{3}{3} : x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{5 π}{6} + πn

(csc^{2} (x) - 2) (3 csc^{2} (x) - 4) = 0

2 sec (x) - 3 tan (x) = - tan (x)

cot (θ) + csc (θ) = - 3

3 tan^{2} (θ) + 1 = \frac{2}{tan ^{2} ( θ )}

4 tan (x) = 2 sec^{2} (x)

What is the general solution for 3sqrt(3)+2tan(x)=2sqrt(3)-tan(x) ?
The general solution for 3sqrt(3)+2tan(x)=2sqrt(3)-tan(x) is x=(5pi)/6+pin