What is the general solution for cos^2(x)-10cos(x)-1=0 ?

The general solution for cos^2(x)-10cos(x)-1=0 is x=1.66997…+2pin,x=-1.66997…+2pin

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cos^2(x)-10cos(x)-1=0

cos^{2} (x) - 10 cos (x) - 1 = 0

x = 1.66997 \dots + 2 πn, x = - 1.66997 \dots + 2 πn

Solution steps

cos^{2} (x) - 10 cos (x) - 1 = 0

Solve by substitution

cos (x) = 5 + 26, cos (x) = 5 - 26

cos (x) = 5 + 26 :

No Solution

cos (x) = 5 - 26 : x = arccos (5 - 26) + 2 πn, x = - arccos (5 - 26) + 2 πn

Combine all the solutions

x = arccos (5 - 26) + 2 πn, x = - arccos (5 - 26) + 2 πn

Show solutions in decimal form

x = 1.66997 \dots + 2 πn, x = - 1.66997 \dots + 2 πn

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

sin^{2} (x) - 2 = 0

0.5 = sin (x)

cos^{2} (θ) + cos (θ) - 1 = 0

sin^{2} (x) - 3 = 0

What is the general solution for cos^2(x)-10cos(x)-1=0 ?
The general solution for cos^2(x)-10cos(x)-1=0 is x=1.66997…+2pin,x=-1.66997…+2pin