What is the general solution for 6tan^2(θ)+10tan(θ)=9tan(θ)+2 ?

The general solution for 6tan^2(θ)+10tan(θ)=9tan(θ)+2 is θ=0.46364…+pin,θ=-0.58800…+pin

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6tan^2(θ)+10tan(θ)=9tan(θ)+2

6 tan^{2} (θ) + 10 tan (θ) = 9 tan (θ) + 2

θ = 0.46364 \dots + πn, θ = - 0.58800 \dots + πn

Solution steps

6 tan^{2} (θ) + 10 tan (θ) = 9 tan (θ) + 2

Solve by substitution

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

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

tan (θ) = - \frac{2}{3} : θ = arctan (- \frac{2}{3}) + πn

Combine all the solutions

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

Show solutions in decimal form

θ = 0.46364 \dots + πn, θ = - 0.58800 \dots + πn

y, z = cos (y)

cos (x) = \frac{64}{83}

2 sin (z) = 1

cos (\frac{π}{2} - θ) = - sin (θ)

tan^{2} (x) + tan (x) = 0, 0 \leq x \leq 2 π

What is the general solution for 6tan^2(θ)+10tan(θ)=9tan(θ)+2 ?
The general solution for 6tan^2(θ)+10tan(θ)=9tan(θ)+2 is θ=0.46364…+pin,θ=-0.58800…+pin