Question

cos 3x + cos x = cos 4x + cos 2x ​

Answer 1

Step-by-step explanation:

apply formula

cos C + cosD = 2cos((C+D)/2)*cos((C-D) /2)

cos3x + cosx = 2cos((3x+x)/2)* cos((3x-x)/2)

= 2cos2x cosx

cos4x + cos2x = 2cos((6x) /2)* cos((2x) /2)

= 2cos3x cosx

joining the equations,

2cos2x cosx= 2cos3x cosx

cos2x= cos3x

cos2x-cos3x =0

applying formula:

cosA - cosB= -2sin((A+B)/2* sin((A-B)/2)

cos2x-cos3x = -2sin((5x) /2)* sin(-(x) /2)

hope this helps