How do you do this problem?

Question

Find all solutions to the equation.

cos^2x + 2 cos x + 1 = 0

Answer 1

Perform a change of variable.

 

y = cos(x)

 

The equation becomes

 

y² + 2y + 1 = 0

 

(y + 1)² = 0

 

y = -1

 

cos(x) = -1

 

x = π ± 2πn,

 

n = any integer