What is the general solution for cos^2(θ)-cos(θ)-1=0 ?

The general solution for cos^2(θ)-cos(θ)-1=0 is θ=2.23703…+2pin,θ=-2.23703…+2pin

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cos^2(θ)-cos(θ)-1=0

cos^{2} (θ) - cos (θ) - 1 = 0

θ = 2.23703 \dots + 2 πn, θ = - 2.23703 \dots + 2 πn

Solution steps

cos^{2} (θ) - cos (θ) - 1 = 0

Solve by substitution

cos (θ) = \frac{1 + 5}{2}, cos (θ) = \frac{1 - 5}{2}

cos (θ) = \frac{1 + 5}{2} :

No Solution

cos (θ) = \frac{1 - 5}{2} : θ = arccos (\frac{1 - 5}{2}) + 2 πn, θ = - arccos (\frac{1 - 5}{2}) + 2 πn

Combine all the solutions

θ = arccos (\frac{1 - 5}{2}) + 2 πn, θ = - arccos (\frac{1 - 5}{2}) + 2 πn

Show solutions in decimal form

θ = 2.23703 \dots + 2 πn, θ = - 2.23703 \dots + 2 πn

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

\frac{18 cos ( 2 θ ) + 27 cos ( θ )}{2} = 0

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

tan (x) sec (x) - 2 tan (x) = 0

- 9 cos^{2} (θ) + 9 = 17 sin (θ) - 8

What is the general solution for cos^2(θ)-cos(θ)-1=0 ?
The general solution for cos^2(θ)-cos(θ)-1=0 is θ=2.23703…+2pin,θ=-2.23703…+2pin