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Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-...

Show that `4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)`

Text Solution

Verified by Experts

`16 sin^(2)27^(@)=8(1-cos 54^(@))`
`=8(1-(sqrt(10-2sqrt(5))/(4))=2(4-sqrt(10-2sqrt(5)))`
`=(5+sqrt(5))+(3-sqrt(5))-2sqrt((5+sqrt(5))(3-sqrt(5)))`
`{sqrt(5+sqrt(5))-sqrt(3-sqrt(5))}^(2`
`rArr 4sin 27^(@)=(sqrt(5+sqrt(5)))-(sqrt(3-sqrt(5)))`
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