Question

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

cos 2x - cos x = 0

Can i have help its urgent

Answer 1

Are you sure is is not cos²x-cosx=0?

Answer 2

(last week I answered the same question, it was cos²x eventually...)

Answer 3

no it says cos 2x

Answer 4

If is is cos 2x - cos x = 0, write as cos 2x = cos x.

Then remember the general form: \[\cos a = \cos b \Leftrightarrow a=\pm b + 2k \pi\]

Answer 5

So you would get:\[2x=x + 2k \pi \vee 2x=-x + 2k \pi\]

Now, these are two separate equations that can easily be solved.
Because the interval is [0, 2pi) you will not have many solutions left.