Ответ:2 + √6 + √2/4
sinA×cosB = 1/2(sin(A+B) + sin(A-B))
Подставляем значения, получаем
2sin22°30`×cos7°30`= 2×1/2(sin(22°30+cos7°30`)+sin(22°30- cos7°30`))= sin 30° + sin 15° = sin 30° + sin(45°-30°) = sin30° + sin45°cos30° - sin30°cos45°= 1/2+√2/2×√3/2 - 1/2×√2/2 = 1/2 + √6/4-√2/4 = 1×2+√6+√2/4 = 2+√6+√2/4