What is the general solution for cot^2(θ)-6cot(θ)+8=0 ?

The general solution for cot^2(θ)-6cot(θ)+8=0 is θ=0.24497…+pin,θ=0.46364…+pin

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cot^2(θ)-6cot(θ)+8=0

cot^{2} (θ) - 6 cot (θ) + 8 = 0

θ = 0.24497 \dots + πn, θ = 0.46364 \dots + πn

Solution steps

cot^{2} (θ) - 6 cot (θ) + 8 = 0

Solve by substitution

cot (θ) = 4, cot (θ) = 2

cot (θ) = 4 : θ = arccot (4) + πn

cot (θ) = 2 : θ = arccot (2) + πn

Combine all the solutions

θ = arccot (4) + πn, θ = arccot (2) + πn

Show solutions in decimal form

θ = 0.24497 \dots + πn, θ = 0.46364 \dots + πn

5 cos (x) = - 2 sin^{2} (x) + 4

4 sin^{2} (x) = 2

csc^{2} (x) = 5 csc (x)

cos (4 θ) = 0

t, L {sin (2 t)} = \frac{2}{s ^{2} + 4}

What is the general solution for cot^2(θ)-6cot(θ)+8=0 ?
The general solution for cot^2(θ)-6cot(θ)+8=0 is θ=0.24497…+pin,θ=0.46364…+pin