Вычислите
sin75°+√3 cos75°

sin(30°+45°)+√3*cos(30°+45°)=sin(30°)*cos(45°)+cos(30°)*sin(45°)+√3*(cos(30°)*cos(45°)-sin(30°)*sin(45°))=1/2*√2/2+√3/2*√2/2+√3*(√3/2*√2/2-1/2*√2/2)=√2/4+√6/4+√3*(√6/4-√2/4=√2/4+√6/4+(√18-√6)/4=(√2+√6+3√2-√6)/4=(4√2)/4=√2