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

The general solution for 2tan^2(θ)+tan(θ)=0 is θ=pin,θ=-0.46364…+pin

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2tan^2(θ)+tan(θ)=0

2 tan^{2} (θ) + tan (θ) = 0

θ = πn, θ = - 0.46364 \dots + πn

Solution steps

2 tan^{2} (θ) + tan (θ) = 0

Solve by substitution

tan (θ) = 0, tan (θ) = - \frac{1}{2}

tan (θ) = 0 : θ = πn

tan (θ) = - \frac{1}{2} : θ = arctan (- \frac{1}{2}) + πn

Combine all the solutions

θ = πn, θ = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

θ = πn, θ = - 0.46364 \dots + πn

2 cos^{2} (θ) + sin (θ) = 1

tan (2 x) - 3 = 0

0 = cos (2 x)

cos (5 x) = 0

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

What is the general solution for 2tan^2(θ)+tan(θ)=0 ?
The general solution for 2tan^2(θ)+tan(θ)=0 is θ=pin,θ=-0.46364…+pin