`cos 18^(@) ,sin 36^(@) sin 72^(@) cos 72^(@) sin 54^(@)` और `cos 54^(@)` के मान ज्ञात कीजिए।

Explanation

`cos 18^(@) =sqrt(1-sin^(2) 18^(@)) =sqrt(1-((sqrt(5)-1)/(4))^(2))`
`=sqrt((16-6+2sqrt(5))/(16) )=sqrt(10+2sqrt(5))/(4)`
`sin 36^(@) = sqrt(1-cos^(2) 36^(@)) = sqrt(1-((sqrt(5)+1)/(4))^(2))`
`=sqrt((16-6-2sqrt(5))/(16) )=sqrt(10-2sqrt(5))/(4)`
`sin 72^(@) =sin (90^(@) -18^(@)) =cos 18^(@) = sqrt((10 +2sqrt(5))/(4))`
`cos 72^(@) =cos (90^(@) -18^(@)) =sin 18^(@) = (sqrt(5)-1)/(4)`
`sin 54^(@) =sin (90^(@) -36^(@)) =cos 36^(@)=(sqrt(5)+1)/(4)`
`cos 54^(@) = cos (90^(@) -36^(@) ) = sin 36^(@) = (sqrt((10 -2sqrt(5))))/(4)`