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

The general solution for cos^2(x)-cos(x)-1=0 is x=2.23703…+2pin,x=-2.23703…+2pin

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

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

x = 2.23703 \dots + 2 πn, x = - 2.23703 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{1 + 5}{2}, cos (x) = \frac{1 - 5}{2}

cos (x) = \frac{1 + 5}{2} :

No Solution

cos (x) = \frac{1 - 5}{2} : x = arccos (\frac{1 - 5}{2}) + 2 πn, x = - arccos (\frac{1 - 5}{2}) + 2 πn

Combine all the solutions

x = arccos (\frac{1 - 5}{2}) + 2 πn, x = - arccos (\frac{1 - 5}{2}) + 2 πn

Show solutions in decimal form

x = 2.23703 \dots + 2 πn, x = - 2.23703 \dots + 2 πn

9 sin (18 x) + 11 = 2

3 sin (2 x) = 0

8 cos^{2} (θ) = 2

tan (2 θ) - 2 sin (θ) = 0

sin (x) cos (x) = 3 cos (x)

What is the general solution for cos^2(x)-cos(x)-1=0 ?
The general solution for cos^2(x)-cos(x)-1=0 is x=2.23703…+2pin,x=-2.23703…+2pin