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

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

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3tan^2(θ)+sqrt(3)tan(θ)=0

3 tan^{2} (θ) + 3 tan (θ) = 0

θ = πn, θ = \frac{5 π}{6} + πn

Solution steps

3 tan^{2} (θ) + 3 tan (θ) = 0

Solve by substitution

tan (θ) = 0, tan (θ) = - \frac{3}{3}

tan (θ) = 0 : θ = πn

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

Combine all the solutions

θ = πn, θ = \frac{5 π}{6} + πn

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

sin (x) cot (x) - sin (x) = 0

tan (θ) = \frac{1}{7}

2 tan (x) + cos (x) = 0

cos (2 x) + sec (2 x) = 11

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