Question

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

cos 4x - cos 2x = 0

Answer 1

cos is a periodic function. the period is \(2\pi\), i.e.
\[ \large \cos x=\cos(x+2k\pi) \]
where k is an integer

Answer 2

What is the upper end of that interval?

Answer 3

o 2pi/3 4pi/3

Answer 4

Apply Cos C - Cos D formula

Answer 5

cos C - Cos D = 2 sin(C+D)/2 Sin(D-C)/2

Answer 6

so 0 pi/3 2pi/3 4pi/3 5pi/3

Answer 7

so 2 Sin3x Sin(-x) =0
either Sin3x=0 or Sin x=0

Answer 8

and use if Sin x=0 then x = n pi, where n =......-2,-1,0,1,2,3....

Answer 9

now it's ok?

Answer 10

im a lil confused what my anserw would be

Answer 11

0 pi/3 2pi/3 4pi/3 5pi/3, pi, 2pi

Answer 12

i think 2 pi is not in the interval...so remove 2 pi

Answer 13

0 pi/3 2pi/3 4pi/3 5pi/3, pi

Answer 14

now it's fine?

Answer 15

either Sin3x=0 or Sin x=0
3x = n pi or x= n pi , where n =...-2,-1,0,1,2,3....

Answer 16

oh ok