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

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

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3tan^2(θ)-1=-2tan(θ)

3 tan^{2} (θ) - 1 = - 2 tan (θ)

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

Solution steps

3 tan^{2} (θ) - 1 = - 2 tan (θ)

Solve by substitution

tan (θ) = \frac{1}{3}, tan (θ) = - 1

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

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

Combine all the solutions

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

Show solutions in decimal form

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

cos (\frac{x}{2}) = \frac{3}{2}, 0 \leq x \leq 2 π

sin (x) = 0.65

sin (x) = 0.78

sin (x) = 0.85

sin (x) = 0.83

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