sin105° =sin(60°+45°)=sin60°cos45°+cos60°*sin45°=
= √3/2 *√2/2+1/2 * √2/2 = √2(√3+1)/4
cos15°=cos(45°-30°)=cos45°cos30°+ sin45°sin30°=
= √2/2 *√3/2 +√2/2* 1/2 =√2(√3 +1)/4
tg75°=tg(30°+45°)= (tg30°+tg45°)/(1-tg30°tg45°)=
= (√3/3+1)/(1-√3/3 *1) =(1+√3/3)/(1-√3/3) =
= (1+√3/3)(1-√3/3)/(1-√3/3)² = (1- 1/3)/(1+1/3 -2√3/3) =
= (2/3)/(4/3 - 2√3/3) = (2/3)/(2/3(2-√3))=1/(2-√3) =
= (2+√3)/(2-√3)(2+√3) =(2+√3)/(4-3)=(2+√3)/1=2+√3