What is the general solution for 6tan^2(θ)-5tan(θ)+1=0 ?

The general solution for 6tan^2(θ)-5tan(θ)+1=0 is θ=0.46364…+pin,θ=0.32175…+pin

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6tan^2(θ)-5tan(θ)+1=0

6 tan^{2} (θ) - 5 tan (θ) + 1 = 0

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

Solution steps

6 tan^{2} (θ) - 5 tan (θ) + 1 = 0

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

6 sin (x) - 24 = 0

- 2 sin (x) - 2 sin (2 x) = 0

\frac{( sin ^{2} ( x ) + 1 )}{1 - sin ^{2} ( x )} - 1 = 2

tan (2 θ) + 3 = 0

- 2 sin (θ) + cos (2 θ) = 1

What is the general solution for 6tan^2(θ)-5tan(θ)+1=0 ?
The general solution for 6tan^2(θ)-5tan(θ)+1=0 is θ=0.46364…+pin,θ=0.32175…+pin