Question

Find all solutions to the equation.

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

Answer 1

Factor the equation.

Answer 2

is it cos=1/2

Answer 3

Nope try again

Answer 4

is it cos - 1/2

Answer 5

and then the solutions are 2pi/3 and 4pi/3

Answer 6

notice is a quadratic equation, and you factor it just like any other quadratic
\(\bf \Large cos^2x + 2 cos x + 1 = 0 \implies a^2+2a+1 = 0\)

Answer 7

i still don't get it

Answer 8

Can you write this ?
\[\cos ^{2}x +2\cos x +1 = \left( \cos x + 1 \right)^{2}\]

Answer 9

what do you mean?

Answer 10

http://www.youtube.com/watch?v=eF6zYNzlZKQ

Answer 11

$$
\tt
\Large{
\cos^2x+2\cos x + 1 =0\\
Let~u=\cos x\\
Then\\
u^2+2u+1=0\\
(u+1)(u+1)=0\\
(u+1)^2=0\\
(u+1)=0\\
u=-1\\
Sub~back~cos(x)~for~u\\
\cos x=-1\\
This~implies~that~x=-\pi ~\pm~2\pi n,~where~n\in\Bbb N.
}
$$
Let me know if you have any questions.