Question

Find all solutions in the interval [0, 2π).

cos2x + 2 cos x + 1 = 0

Answer 1

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

Answer 2

this is a quadratic equation which will factorise

Answer 3

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

Answer 4

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

Answer 5

what about 0 as a solution?

Answer 6

no sorry - its -1

Answer 7

cos 0 = 1 of course

Answer 8

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

Answer 9

are you sure you have the correct question

is it cos 2x or cos^2 x ?

Answer 10

it is cos^2 x

Answer 11

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

Answer 12

in that case the answer is as Stiwam said

Answer 13

thankyou!

Answer 14

yw