What is the general solution for tan^2(θ)+4tan(θ)=3 ?

The general solution for tan^2(θ)+4tan(θ)=3 is θ=0.57338…+pin,θ=-1.35878…+pin

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tan^2(θ)+4tan(θ)=3

tan^{2} (θ) + 4 tan (θ) = 3

θ = 0.57338 \dots + πn, θ = - 1.35878 \dots + πn

Solution steps

tan^{2} (θ) + 4 tan (θ) = 3

Solve by substitution

tan (θ) = - 2 + 7, tan (θ) = - 2 - 7

tan (θ) = - 2 + 7 : θ = arctan (- 2 + 7) + πn

tan (θ) = - 2 - 7 : θ = arctan (- 2 - 7) + πn

Combine all the solutions

θ = arctan (- 2 + 7) + πn, θ = arctan (- 2 - 7) + πn

Show solutions in decimal form

θ = 0.57338 \dots + πn, θ = - 1.35878 \dots + πn

3 cot (θ) + 7 = 0

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

sin^{2} (x) - cos (x) - 1 = 0

3 tan (2 θ) + 1 = 0

sin^{2} (x) - cos (x) = 0

What is the general solution for tan^2(θ)+4tan(θ)=3 ?
The general solution for tan^2(θ)+4tan(θ)=3 is θ=0.57338…+pin,θ=-1.35878…+pin