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

The general solution for tan^2(θ)-6tan(θ)+5=0 is θ=1.37340…+pin,θ= pi/4+pin

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tan^2(θ)-6tan(θ)+5=0

tan^{2} (θ) - 6 tan (θ) + 5 = 0

θ = 1.37340 \dots + πn, θ = \frac{π}{4} + πn

Solution steps

tan^{2} (θ) - 6 tan (θ) + 5 = 0

Solve by substitution

tan (θ) = 5, tan (θ) = 1

tan (θ) = 5 : θ = arctan (5) + πn

tan (θ) = 1 : θ = \frac{π}{4} + πn

Combine all the solutions

θ = arctan (5) + πn, θ = \frac{π}{4} + πn

Show solutions in decimal form

θ = 1.37340 \dots + πn, θ = \frac{π}{4} + πn

tan (4 θ) = - 1

cot (x) (tan (x) - 1) = 0

4 cos^{2} (x) - 3 = - 1

tan (x) = 2.5

y, arctan (y) = x

What is the general solution for tan^2(θ)-6tan(θ)+5=0 ?
The general solution for tan^2(θ)-6tan(θ)+5=0 is θ=1.37340…+pin,θ= pi/4+pin