Question

Find all solutions to the equation in the interval [0, 2π).
cos 2x - cos x = 0

Answer 1

so, cos2x=cosx, I think x is in those special angles

Answer 2

use identity : cos2x=2cos^2 x - 1

Answer 3

so, we have a quadratic equation in form cosx,
2cos^2 x - 1 - cosx = 0 or
2cos^2 x - cosx - 1 = 0
can u factor out it

Answer 4

ok I get cos x(2 cos x-1)=1

Answer 5

np, it should be
(2cosx + 1)(cosx - 1) = 0

Answer 6

now, for zeroes take each factors be zero, so
2cosx+1=0 or cosx-1=0
solve for x

Answer 7

ok I got the solutions 0, 2pi/3 and 4pi/3

Answer 8

thank you

Answer 9

but, i miss one root :)

Answer 10

looks 0 be same for 2pi, right ?

Answer 11

I got the answer right

Answer 12

ok, great..