What is the general solution for -3tan^2(θ)+2tan(θ)=6tan(θ)+1 ?

The general solution for -3tan^2(θ)+2tan(θ)=6tan(θ)+1 is θ=(3pi)/4+pin,θ=-0.32175…+pin

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-3tan^2(θ)+2tan(θ)=6tan(θ)+1

- 3 tan^{2} (θ) + 2 tan (θ) = 6 tan (θ) + 1

θ = \frac{3 π}{4} + πn, θ = - 0.32175 \dots + πn

Solution steps

- 3 tan^{2} (θ) + 2 tan (θ) = 6 tan (θ) + 1

Solve by substitution

tan (θ) = - 1, tan (θ) = - \frac{1}{3}

tan (θ) = - 1 : θ = \frac{3 π}{4} + πn

tan (θ) = - \frac{1}{3} : θ = arctan (- \frac{1}{3}) + πn

Combine all the solutions

θ = \frac{3 π}{4} + πn, θ = arctan (- \frac{1}{3}) + πn

Show solutions in decimal form

θ = \frac{3 π}{4} + πn, θ = - 0.32175 \dots + πn

sin (x) + cos (x) = - 3

sin (x) = \frac{1}{2}, cos (x) = - \frac{3}{2}

cos (x) = \frac{2 5}{5}

csc (x) = cot (x) - 1

2 cos (θ) + 1 = sec (θ)

What is the general solution for -3tan^2(θ)+2tan(θ)=6tan(θ)+1 ?
The general solution for -3tan^2(θ)+2tan(θ)=6tan(θ)+1 is θ=(3pi)/4+pin,θ=-0.32175…+pin