Question

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

cos 4x - cos 2x = 0
i dont get how to solve this

Answer 1

cos is a periodic function. the period is 2π, i.e.

cosx=cos(x+2kπ)

where k is an integer

Answer 2

which integer do i use? 4 or 2

Answer 3

2pi/3 4pi/3 I think

Answer 4

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

Answer 5

what formula is rthat?!

Answer 6

what is c and what is d\

Answer 7

lol it would be a long explanation but the answer would amount to
either Sin3x=0 or Sin x=0 3x = n pi or x= n pi , where n =...-2,-1,0,1,2,3....

Answer 8

i hope this helps some how

cos 4 x - cos 2 x = 0

2cos^2 2x-1 - cos 2x = 0

2u^2 -u -1 = 0

(u-1)(2u+1) = 0

u = 1; u = -1/2

cos 2x = 1 ; cos 2x = -1/2

2x = 0 ; 2x = pi-pi/3, 2x = pi + pi/3

x = 0 + npi; x = pi/3 + npi, x = 2pi/3 + npi

x = 0, pi; x = pi/3, 4pi/3, x = 2pi/3, 5pi/3

so solutions will be : x = 0, pi/3, 2pi/3, 4pi/3, 5pi/3, pi

Answer 9

@lbouskila

Answer 10

thank you!

Answer 11

:) welcome