`sin .( 23pi)/( 24)` का मान निकालें

Explanation

`sin. ( 23pi)/(24)= sin( pi- ( pi)/24) = sin. ( pi)/( 24) = sin 7. (1^(@))/(2)`
माना कि `theta = 7(1^(@))/(2),` तो `2 theta = 15^(@)`
अब `sin^(2) theta = ( 1 - cos 2 theta)/( 2 ) = (1)/(2) ( 1- cos15^(@))`
`= (1)/(2) ( 1- ( sqrt(3)+1)/(2sqrt(2))) = (1)/(2) (( 2sqrt(2) - sqrt(3) -1)/(sqrt(2)))`
`=( 2sqrt(2) -sqrt(3) -1)/(4sqrt(2))`
` :' sin theta = sin 7 (1^(@))/(2) gt0 `
`:. sin 7 ( 1^(@))/(2) = sqrt((2sqrt(2)- sqrt(3)-1)/( 4 sqrt(2)))= (1)/(4) sqrt(8-2sqrt(6) - 2 sqrt(2))`
अंश तथा हर को से गुणा करने पर |