What is the general solution for 2tan^2(θ)-3tan(θ)+1=0 ?

The general solution for 2tan^2(θ)-3tan(θ)+1=0 is θ= pi/4+pin,θ=0.46364…+pin

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2tan^2(θ)-3tan(θ)+1=0

2 tan^{2} (θ) - 3 tan (θ) + 1 = 0

θ = \frac{π}{4} + πn, θ = 0.46364 \dots + πn

Solution steps

2 tan^{2} (θ) - 3 tan (θ) + 1 = 0

Solve by substitution

tan (θ) = 1, tan (θ) = \frac{1}{2}

tan (θ) = 1 : θ = \frac{π}{4} + πn

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

Combine all the solutions

θ = \frac{π}{4} + πn, θ = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

θ = \frac{π}{4} + πn, θ = 0.46364 \dots + πn

cos (x) = \frac{9}{17}

- 6 sin (c) + 0 = sin (c) - 3

tan (x) = \frac{11}{12}

2 cos (a) + 3 = 4

tan (x) cot (x) - 3 tan (x) = 0

What is the general solution for 2tan^2(θ)-3tan(θ)+1=0 ?
The general solution for 2tan^2(θ)-3tan(θ)+1=0 is θ= pi/4+pin,θ=0.46364…+pin