## mgarcia634 3 years ago Find all solutions in the interval [0, 2π). cos2x + 2 cos x + 1 = 0

1. mgarcia634

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

2. cwrw238

this is a quadratic equation which will factorise

3. Stiwan

$\cos²(x) + 2\cos(x) + 1 = (\cos(x) + 1)²$ Hence the roots are all x out of [0,2pi) for which cos(x) = -1. -pi and pi

4. Stiwan

Sorry, of course it's just + pi as there are no negative numbers in this interval

5. cwrw238

what about 0 as a solution?

6. cwrw238

no sorry - its -1

7. cwrw238

cos 0 = 1 of course

8. mgarcia634

the answer choices are a) x=2pi B)x=pi c) x=pi/4, 7pi/4

9. cwrw238

are you sure you have the correct question is it cos 2x or cos^2 x ?

10. mgarcia634

it is cos^2 x

11. Stiwan

It's B) x = pi as in my answer.

12. cwrw238

in that case the answer is as Stiwam said

13. mgarcia634

thankyou!

14. cwrw238

yw