What is the general solution for cot^2(θ)+cot(θ)-20=0 ?

The general solution for cot^2(θ)+cot(θ)-20=0 is θ=0.24497…+pin,θ=2.94419…+pin

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cot^2(θ)+cot(θ)-20=0

cot^{2} (θ) + cot (θ) - 20 = 0

θ = 0.24497 \dots + πn, θ = 2.94419 \dots + πn

Solution steps

cot^{2} (θ) + cot (θ) - 20 = 0

Solve by substitution

cot (θ) = 4, cot (θ) = - 5

cot (θ) = 4 : θ = arccot (4) + πn

cot (θ) = - 5 : θ = arccot (- 5) + πn

Combine all the solutions

θ = arccot (4) + πn, θ = arccot (- 5) + πn

Show solutions in decimal form

θ = 0.24497 \dots + πn, θ = 2.94419 \dots + πn

cos (2 x) + 2 cos (x) + 1 = 0

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

arcsin (x) = \frac{π}{2}

sin (θ) = 0.6

2 sin (x) tan (x) = - 3 tan (x)

What is the general solution for cot^2(θ)+cot(θ)-20=0 ?
The general solution for cot^2(θ)+cot(θ)-20=0 is θ=0.24497…+pin,θ=2.94419…+pin