Home
Class 11
MATHS
Prove that 4cos12^@cos48^@cos72^@=cos36^...

Prove that `4cos12^@cos48^@cos72^@=cos36^@`

Text Solution

Verified by Experts

Here, we will use the following rules,
`2cosAcosB = cos(A+B)+cos(A-B)`
`cosA+cos B = 2cos((A+B)/2)cos((A-B)/2)`
`L.H.S. = 4cos12^@cos48^@cos72^@`
`=2cos72^@(cos(48+12)^@+cos(48-12)^@)`
`=2cos72^@(cos60^@+cos36^@)`
`=2cos72^@(1/2+cos36^@)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that: 4"cos"12^0cos48^0cos72^0=cos36^0

Prove that: 4cos12^(0)cos48^(0)cos72^(0)=cos36^(@)

Prove that: i) cos10^(@)cos30^(@)cos50^(@)cos70^(@)=3/16 ii) cos20^(@)cos40^(@)cos60^(@)cos80^(@)=1/16 iii) 4cos12^(@)cos48^(@)cos72^(@)=cos36^(@) iv) cos40^(@) cos80^(@)cos160^(@)=-1/8

Prove that: i) cos10^(@)cos30^(@)cos50^(@)cos70^(@)=3/16 ii) cos20^(@)cos40^(@)cos60^(@)cos80^(@)=1/16 iii) 4cos12^(@)cos48^(@)cos72^(@)=cos36^(@) iv) cos40^(@) cos80^(@)cos160^(@)=-1/8

cos48^(@)*cos12^(@)=

cos48^(@)*cos12^(@)=

cos12^(@)cos24^(@)cos48^(@)cos84^(@)

Prove that (sin18^(@))/(cos72^(@))=1

Prove that cos36^(@)cos72^(@)cos108^(@)cos144^(@)=1//16 .