SOLUTION: Solve the equation for exact solutions over the interval [0, 2π). cos^2 x + 2 cos x + 1 = 0

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation for exact solutions over the interval [0, 2π). cos^2 x + 2 cos x + 1 = 0      Log On


   

Question 1043292: Solve the equation for exact solutions over the interval [0, 2π).
cos^2 x + 2 cos x + 1 = 0
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve the equation for exact solutions over the interval [0, 2π).
cos^2 (x) + 2 cos (x) + 1 = 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` 

cos%5E2%28x%29+%2B+2cos%28x%29+%2B+1 = 0,  --->  ( apply the formula a%5E2+%2B+2a+%2B+1 = %28a%2B1%29%5E2 )  --->

%28cos%28x%29%2B1%29%5E2 = 0,  --->

cos(x) + 1 = 0  --->

cos(x) = -1  --->

x = pi.

Answer.  x = pi.

Solved.