Question

cosø. Cos2ø. Cos3ø=1/4

Answer 1

hi

Here is your Answer!

cosxcos2xcos3x=1/4
==>
4cosx cos 2x cos3x = 1
divide 4 into 2× 2 terms
then
==>
(2cosxcos3x)(2cos2x)=1
==>
(cos4x+cos2x)(2cos2x)=1
==>
2cos4xcos2x+(2cos²2x-1)=0
==>
2cos4xcos2x+cos4x=0
==>
cos4x(2cos2x+1)=0
==>
Either, cos4x=0
==>
4x=(2n+1)π/2
==>
x=(2n+1)π/8
==>
2cos2x+1=0
==>
2cos2x=-1
==>
cos2x=-1/2
==>
cos2x=cos(-π/3)
==>
cos2x=cosπ/3

[neglecting the negative sign for cos]
2x=2nπ plus minus π/3
x=nπ plus minus π/6

Hope it's helpful ✌