Question

Упростите sin75*cos15

Answer 1

sin(45+30)*cos(45-30)=(sin45cos30+sin30cos45)*(cos45cos30+sin45sin30)=

=(√2/2*√3/2+1/2*√2/2)*(√2/2*√3/2+√2/2*1/2)=(√2/2*√3/2+√2/2*1/2)²=

=(√6/4+√2/4)²=((√6+√2)/4)²=(6+2√12+2)/16=(8+4√3)/16=(2+√3)/4.