What is the general solution for 6tan^2(θ)-10tan(θ)+1=-5tan(θ) ?

The general solution for 6tan^2(θ)-10tan(θ)+1=-5tan(θ) is θ=0.46364…+pin,θ=0.32175…+pin

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6tan^2(θ)-10tan(θ)+1=-5tan(θ)

6 tan^{2} (θ) - 10 tan (θ) + 1 = - 5 tan (θ)

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

Solution steps

6 tan^{2} (θ) - 10 tan (θ) + 1 = - 5 tan (θ)

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

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

2 sin (2 x) + 6 sin (x) - 2 cos (x) = 3

sin (2 x) = \frac{4}{5}

2 csc (x) + 17 = 15 + csc (x)

cos (x) - sin (x) = 2

cot (θ) = (5.8473)

What is the general solution for 6tan^2(θ)-10tan(θ)+1=-5tan(θ) ?
The general solution for 6tan^2(θ)-10tan(θ)+1=-5tan(θ) is θ=0.46364…+pin,θ=0.32175…+pin