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

Options

A. `(sqrt(3+sqrt(5))+sqrt(5-sqrt(5)))/(4)`
B. `(sqrt(3+sqrt(5))+sqrt(5+sqrt(5)))/(4)`
C. `(sqrt(3-sqrt(5))+sqrt(5-sqrt(5)))/(4)`
D. `(sqrt(3+sqrt(5))-sqrt(5-sqrt(5)))/(4)`

Answer

A

Explanation

`becausesin18^(@)=(sqrt(5)-1)/(4)`
`x^(2)=4^(2)-(sqrt(5)-1)^(2)`
`rArrx=sqrt(10+2sqrt(5))`
`rArrcos18^(@)=(sqrt(10+2sqrt(5)))/(4)`
`rArr2cos^(2)9-1=(sqrt(10+2sqrt(5)))/(4)`
`cos^(2)9=(sqrt(10+2sqrt(5))+4)/(8)`
`rArrsin^(2)81=(4+sqrt(10+2sqrt(5)))/(8)`
After squaring all the options available , we come to conclusion that option (a) is correct.