1. Преобразовать в произведение

а) sin105° + sin75°

б) cos П/12 + sin 7 П/12

2. Преобразовать в сумму

а) sin 37°30' * sin 7°30'

б) cos 75° * cos 105°

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