What is the general solution for -9tan^2(θ)-1=-6tan(θ) ?

The general solution for -9tan^2(θ)-1=-6tan(θ) is θ=0.32175…+pin

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-9tan^2(θ)-1=-6tan(θ)

- 9 tan^{2} (θ) - 1 = - 6 tan (θ)

θ = 0.32175 \dots + πn

Solution steps

- 9 tan^{2} (θ) - 1 = - 6 tan (θ)

Solve by substitution

tan (θ) = \frac{1}{3}

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

Combine all the solutions

θ = arctan (\frac{1}{3}) + πn

Show solutions in decimal form

θ = 0.32175 \dots + πn

2 cos (2 θ) - 1 = 0

4 cos (2 x) - 1 = 0

cos (x) sin (x) = 0

3 tan^{2} (θ) = 1

3 cos (x) = 2 sin^{2} (x)

What is the general solution for -9tan^2(θ)-1=-6tan(θ) ?
The general solution for -9tan^2(θ)-1=-6tan(θ) is θ=0.32175…+pin