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

The general solution for cos^2(θ)-2cos(θ)-1=0 is θ=1.99787…+2pin,θ=-1.99787…+2pin

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cos^2(θ)-2cos(θ)-1=0

cos^{2} (θ) - 2 cos (θ) - 1 = 0

θ = 1.99787 \dots + 2 πn, θ = - 1.99787 \dots + 2 πn

Solution steps

cos^{2} (θ) - 2 cos (θ) - 1 = 0

Solve by substitution

cos (θ) = 1 + 2, cos (θ) = 1 - 2

cos (θ) = 1 + 2 :

No Solution

cos (θ) = 1 - 2 : θ = arccos (1 - 2) + 2 πn, θ = - arccos (1 - 2) + 2 πn

Combine all the solutions

θ = arccos (1 - 2) + 2 πn, θ = - arccos (1 - 2) + 2 πn

Show solutions in decimal form

θ = 1.99787 \dots + 2 πn, θ = - 1.99787 \dots + 2 πn

tan (θ) = \frac{9.5}{6.4}

sin (x) cos (x) - \frac{1}{2} cos (x) = 0

sin (x + \frac{π}{3}) - sin (x - \frac{π}{3}) = 0

- tan (2 x) + 2 sin (x) = 0

10 tan (a) + 8 = 5 tan (a) + 3

What is the general solution for cos^2(θ)-2cos(θ)-1=0 ?
The general solution for cos^2(θ)-2cos(θ)-1=0 is θ=1.99787…+2pin,θ=-1.99787…+2pin