What is the general solution for cos^2(θ)-6cos(θ)+1=0 ?

The general solution for cos^2(θ)-6cos(θ)+1=0 is θ=1.39837…+2pin,θ=2pi-1.39837…+2pin

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cos^2(θ)-6cos(θ)+1=0

cos^{2} (θ) - 6 cos (θ) + 1 = 0

θ = 1.39837 \dots + 2 πn, θ = 2 π - 1.39837 \dots + 2 πn

Solution steps

cos^{2} (θ) - 6 cos (θ) + 1 = 0

Solve by substitution

cos (θ) = 3 + 22, cos (θ) = 3 - 22

cos (θ) = 3 + 22 :

No Solution

cos (θ) = 3 - 22 : θ = arccos (3 - 22) + 2 πn, θ = 2 π - arccos (3 - 22) + 2 πn

Combine all the solutions

θ = arccos (3 - 22) + 2 πn, θ = 2 π - arccos (3 - 22) + 2 πn

Show solutions in decimal form

θ = 1.39837 \dots + 2 πn, θ = 2 π - 1.39837 \dots + 2 πn

4 = 6 sec (x)

cot (3 θ) + 1 = csc (3 θ)

sin (a) = - \frac{1}{2}

tan (a) + sec (a) = 2

sin (θ) = \frac{5}{11}

What is the general solution for cos^2(θ)-6cos(θ)+1=0 ?
The general solution for cos^2(θ)-6cos(θ)+1=0 is θ=1.39837…+2pin,θ=2pi-1.39837…+2pin