Question

1. Преобразовать в произведение
а) sin105° + sin75°
б) cos П/12+ sin 7П/12

2. Преобразовать в сумму
а) sin 37°30' * sin 7°30'
б) cos 75° * cos 105°

Answer 1

1.a) =2sin(105°+75°)/2×cos(105°-75°)/2=2sin90°×cos15°=2cos15°
b)= sin(π/2-π/12)+sin7π/12=2sin(π/2-π/12+7π/12)/2×cos(π/2π/127π12)   = 2sin0×cos(-π)=0
2/a)=1/2(cos(37°30`-7°30`)-cos(37°30`+7°30`))=1/2(cos30°-cos45°)=1/2(√3/2-√2/2)=
√3/4-√2/4
b)=1/2(cos(75+105)+cos(75-105))=1/2(cos180+cos30)=1/2(-1+√3/2)=-1/2+√3/2