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

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

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

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

x = π + 2 πn

Solution steps

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

Solve by substitution

cos (x) = - 1

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

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

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

\frac{1}{( sec ^{2} ( a ) )} + \frac{1}{( cos ^{2} ( a ) )} = 1

(1 - cos (a)) (1 + cos (a)) = tan (a) sin (a)

tan^{2} (x) + \frac{1}{6} + \frac{tan ( 1 )}{3} = 0

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