Sin75° = Sin(30° + 45°)
= Sin30°.Cos45° + Sin45°.Cos30°
= 1/2 . √2/2 + √2/2.√3/2
= √2/2 ( 1/2 + √3/2 )
= √2/2 ((1+√3 ) /2 )
= (√2 + √6 )/ 4