What is the general solution for sqrt(3)tan^2(x)+tan(x)=0 ?

The general solution for sqrt(3)tan^2(x)+tan(x)=0 is x=pin,x=(5pi)/6+pin

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sqrt(3)tan^2(x)+tan(x)=0

3 tan^{2} (x) + tan (x) = 0

x = πn, x = \frac{5 π}{6} + πn

Solution steps

3 tan^{2} (x) + tan (x) = 0

Solve by substitution

tan (x) = 0, tan (x) = - \frac{3}{3}

tan (x) = 0 : x = πn

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

Combine all the solutions

x = πn, x = \frac{5 π}{6} + πn

tan^{2} (x) - 4 sin (x) + 4 = 0

\frac{1}{sin ( x )} + \frac{1}{cos ( x )} = 0

1 - cos (2 x) = 0

sin (x) = \frac{37}{64}

1 = 4 tan (- \frac{4}{81} + c)

What is the general solution for sqrt(3)tan^2(x)+tan(x)=0 ?
The general solution for sqrt(3)tan^2(x)+tan(x)=0 is x=pin,x=(5pi)/6+pin