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

The general solution for tan^2(x)-3tan(x)+1=0 is x=1.20593…+pin,x=0.36486…+pin

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tan^2(x)-3tan(x)+1=0

tan^{2} (x) - 3 tan (x) + 1 = 0

x = 1.20593 \dots + πn, x = 0.36486 \dots + πn

Solution steps

tan^{2} (x) - 3 tan (x) + 1 = 0

Solve by substitution

tan (x) = \frac{3 + 5}{2}, tan (x) = \frac{3 - 5}{2}

tan (x) = \frac{3 + 5}{2} : x = arctan (\frac{3 + 5}{2}) + πn

tan (x) = \frac{3 - 5}{2} : x = arctan (\frac{3 - 5}{2}) + πn

Combine all the solutions

x = arctan (\frac{3 + 5}{2}) + πn, x = arctan (\frac{3 - 5}{2}) + πn

Show solutions in decimal form

x = 1.20593 \dots + πn, x = 0.36486 \dots + πn

sin (θ) + sin (2 θ) = 0

tan^{2} (θ) sin (θ) = - sin (θ)

sec (x) = 1 + tan (x)

cos^{2} (x) = 0, 5

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

What is the general solution for tan^2(x)-3tan(x)+1=0 ?
The general solution for tan^2(x)-3tan(x)+1=0 is x=1.20593…+pin,x=0.36486…+pin