How do you use sum and difference identities to find the exact value of sin75?

trun it into sin( 45 + 30 ).

sin ( 45 + 30 ) = sin30cos45 + cos30sin45

sin30cos45 + cos30sin45 = (1/2)((sqrroot2)/2) + ((sqrroot3)/2)((sqrroot2)/2)

(1/2)((sqrroot2)/2) +((sqrroot3)/2)((sqrroot2)/2)=((sqrroot2)/4) + ((sqrroot6)/4)

((sqrroot2)/4) + ((sqrroot6)/4)= ((sqrroot2) + (sqrroot6)) /4