What is the general solution for cos^2(x)-4cos(x)-1=0 ?

The general solution for cos^2(x)-4cos(x)-1=0 is x=1.80911…+2pin,x=-1.80911…+2pin

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cos^2(x)-4cos(x)-1=0

cos^{2} (x) - 4 cos (x) - 1 = 0

x = 1.80911 \dots + 2 πn, x = - 1.80911 \dots + 2 πn

Solution steps

cos^{2} (x) - 4 cos (x) - 1 = 0

Solve by substitution

cos (x) = 2 + 5, cos (x) = 2 - 5

cos (x) = 2 + 5 :

No Solution

cos (x) = 2 - 5 : x = arccos (2 - 5) + 2 πn, x = - arccos (2 - 5) + 2 πn

Combine all the solutions

x = arccos (2 - 5) + 2 πn, x = - arccos (2 - 5) + 2 πn

Show solutions in decimal form

x = 1.80911 \dots + 2 πn, x = - 1.80911 \dots + 2 πn

- 9 sin (3 x) = 0

cos (4 x) - 7 cos (2 x) = 8

6 tan (B) + 14 = 0

- 4 tan^{2} (θ) - 4 tan (θ) - 9 = 8 tan (θ) - 4

cot (4 x) = - \frac{3}{3}

What is the general solution for cos^2(x)-4cos(x)-1=0 ?
The general solution for cos^2(x)-4cos(x)-1=0 is x=1.80911…+2pin,x=-1.80911…+2pin