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

The general solution for cos^2(x)-6cos(x)-1=0 is x=1.73379…+2pin,x=-1.73379…+2pin

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cos^2(x)-6cos(x)-1=0

cos^{2} (x) - 6 cos (x) - 1 = 0

x = 1.73379 \dots + 2 πn, x = - 1.73379 \dots + 2 πn

Solution steps

cos^{2} (x) - 6 cos (x) - 1 = 0

Solve by substitution

cos (x) = 3 + 10, cos (x) = 3 - 10

cos (x) = 3 + 10 :

No Solution

cos (x) = 3 - 10 : x = arccos (3 - 10) + 2 πn, x = - arccos (3 - 10) + 2 πn

Combine all the solutions

x = arccos (3 - 10) + 2 πn, x = - arccos (3 - 10) + 2 πn

Show solutions in decimal form

x = 1.73379 \dots + 2 πn, x = - 1.73379 \dots + 2 πn

tan (5 x) tan (x) = tan (5 x)

4 sin^{2} (x) = 1 + 4 cos (x)

4 sec (θ) + 23 = sec (θ)

2 cos (3 x) - 3 = 0

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

What is the general solution for cos^2(x)-6cos(x)-1=0 ?
The general solution for cos^2(x)-6cos(x)-1=0 is x=1.73379…+2pin,x=-1.73379…+2pin