SOLUTION: Solve the equation for exact solutions over the interval [0, 2π). cos2x + 2 cos x + 1 = 0

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Question 1043276: Solve the equation for exact solutions over the interval [0, 2π).
cos2x + 2 cos x + 1 = 0
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve the equation for exact solutions over the interval [0, 2π).
cos2x + 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.

Or, if your original equation is cos%282x%29+%2B+cos%28x%29+%2B+1 = 0,
then see the solution under this link
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.906637.html

https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.906637.html