What is the general solution for cos^2(x)-8cos(x)-1=0 ?

The general solution for cos^2(x)-8cos(x)-1=0 is x=1.69421…+2pin,x=-1.69421…+2pin

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cos^2(x)-8cos(x)-1=0

cos^{2} (x) - 8 cos (x) - 1 = 0

x = 1.69421 \dots + 2 πn, x = - 1.69421 \dots + 2 πn

Solution steps

cos^{2} (x) - 8 cos (x) - 1 = 0

Solve by substitution

cos (x) = 4 + 17, cos (x) = 4 - 17

cos (x) = 4 + 17 :

No Solution

cos (x) = 4 - 17 : x = arccos (4 - 17) + 2 πn, x = - arccos (4 - 17) + 2 πn

Combine all the solutions

x = arccos (4 - 17) + 2 πn, x = - arccos (4 - 17) + 2 πn

Show solutions in decimal form

x = 1.69421 \dots + 2 πn, x = - 1.69421 \dots + 2 πn

cos (x) + 2 = 1

2 cos (2 θ) = - 1

3 cot^{2} (x) = 3 cot (x)

sin (7 x) = \frac{3}{2}

- 1.9 sin (t) = 0.4 cos (2 t)

What is the general solution for cos^2(x)-8cos(x)-1=0 ?
The general solution for cos^2(x)-8cos(x)-1=0 is x=1.69421…+2pin,x=-1.69421…+2pin