What is the general solution for -6tan^2(θ)+4tan(θ)=-tan(θ)+1 ?

The general solution for -6tan^2(θ)+4tan(θ)=-tan(θ)+1 is θ=0.32175…+pin,θ=0.46364…+pin

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-6tan^2(θ)+4tan(θ)=-tan(θ)+1

- 6 tan^{2} (θ) + 4 tan (θ) = - tan (θ) + 1

θ = 0.32175 \dots + πn, θ = 0.46364 \dots + πn

Solution steps

- 6 tan^{2} (θ) + 4 tan (θ) = - tan (θ) + 1

Solve by substitution

tan (θ) = \frac{1}{3}, tan (θ) = \frac{1}{2}

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

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

Combine all the solutions

θ = arctan (\frac{1}{3}) + πn, θ = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

θ = 0.32175 \dots + πn, θ = 0.46364 \dots + πn

8 cos^{2} (x) + 14 cos (x) + 3 = 0

0 = 4 cos (x) sin (x) - sin (x)

sin (x) cos (x) = tan (x)

cos (x) = \frac{2}{4}

sin (x) - sin (x) \cdot cos (x) = 0

What is the general solution for -6tan^2(θ)+4tan(θ)=-tan(θ)+1 ?
The general solution for -6tan^2(θ)+4tan(θ)=-tan(θ)+1 is θ=0.32175…+pin,θ=0.46364…+pin