Question

Преобразовать в произведение
а) sin105+sin75
б) cos п/12 * sin 7п/12

Answer 1

sin105+sin75=2 sin90 cos15=2 cos15=2cos(45-30)=2(cos45 cos30+sin45 sin30)=

2(√2/2 *√3/2+√2/2 *1/2)=√6/2+√2/2=(√6-√2)/2

 

 

cosπ/12 *sin7π/12=1/2[sin8π/12+sin6π/12]= 1/2[sin2π/3+sinπ/2]=1/2( √3/2+1)