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

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

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cos^2(x)=cos(x)+1

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

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

Solution steps

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

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

6 sin^{2} (x) = 7 - 5 cos (x)

3 + 3 cos (x) = 2 (1 - cos^{2} (x))

sin (x) = 1.5

cot^{2} (θ) - 4 csc (θ) = - 5

tan (θ) = \frac{2}{7}

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