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If `sin 18^@=(sqrt(5)-1)/4` then what is the value of `sin 81^@`

Answer» `Sin 18^@ = (sqrt5 - 1)/4`
`cos 18^@ = sqrt(1- sin^2 18)`
`= sqrt(1- ((sqrt5-1)/4)^2)`
`= sqrt((16-5-1+ 2sqrt5)/16)= sqrt((10+ 2 sqrt5)/16)`
`cos 18^@ = sqrt((10 + 2 sqrt5)/4)`
`sin 81^@ = sin(90- 9)= cos9^@`
`cos 9^@ = sqrt((1+ cos18^@)/2)`
`cos 9^@ = sqrt(((4+ sqrt(10+2sqrt5))/4)/2)`
`cos 9^@ = sqrt((4+ sqrt(10 + 2 sqrt5))/8)`
`sin 81^@ = cos 9^@ = sqrt(1/2 + sqrt(10+2 sqrt5)/8)`
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