What is the general solution for 3=cot^2(θ)+4cot(θ) ?

The general solution for 3=cot^2(θ)+4cot(θ) is θ=0.99741…+pin,θ=2.92957…+pin

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3=cot^2(θ)+4cot(θ)

3 = cot^{2} (θ) + 4 cot (θ)

θ = 0.99741 \dots + πn, θ = 2.92957 \dots + πn

Solution steps

3 = cot^{2} (θ) + 4 cot (θ)

Switch sides

cot^{2} (θ) + 4 cot (θ) = 3

Solve by substitution

cot (θ) = - 2 + 7, cot (θ) = - 2 - 7

cot (θ) = - 2 + 7 : θ = arccot (- 2 + 7) + πn

cot (θ) = - 2 - 7 : θ = arccot (- 2 - 7) + πn

Combine all the solutions

θ = arccot (- 2 + 7) + πn, θ = arccot (- 2 - 7) + πn

Show solutions in decimal form

θ = 0.99741 \dots + πn, θ = 2.92957 \dots + πn

cos^{2} (2 x) + 3 sin (2 x) - 3 = 0

1 - cos^{2} (x) = 0.75 1 - cos^{2} (y)

sec^{2} (x) - 6 tan (x) + 4 = 0

1 - cos (x) = 2 - 2 sin^{2} (x)

- 5 tan (x) - 12 = tan (x) - 8

What is the general solution for 3=cot^2(θ)+4cot(θ) ?
The general solution for 3=cot^2(θ)+4cot(θ) is θ=0.99741…+pin,θ=2.92957…+pin