Question

cos 4x - cos 2x = 0
Find all solutions to the equation in the interval [0, 2ð).
ð, pi/3 2pi/3 4pi/3 5pi/3, 0?
Is that correct?

Answer 1

\(\cos^4 x - \cos^2x = 0\)

is the equation like above ?

Answer 2

No, Cos(4x)-cos(2x)=0

Answer 3

@ganeshie8 no idea?:(

Answer 4

could u show me ur work

Answer 5

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

Answer 6

So 0, pi/3, 2pi/3, 4pi/3, 5pi/3 and ð

Answer 7

@anas2000 can you help?:D

Answer 8

hmm that doesnt help me

Answer 9

@UnkleRhaukus @robtobey

Answer 10

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


looks you got the same solutions wid very less effort... !

Answer 11

Thank you! Haha

Answer 12

np... yw :) good work !