Question

Обчислити sin 330 ×cos240-sin 225 ×sin 135

Answer 1

sin330° = sin(360° - 30°) = sin(-30°) = -sin30° = -1/2

cos240° = cos(180° + 60°) = -cos60° = -1/2

sin225° = sin(180° + 45°) = -sin45° = -√2/2

sin135° = sin(180° - 45°) = sin45° = √2/2

Тогда получаем:

sin330°·sin240° - sin225°·sin135° = -1/2·(-1/2) - (-√2/2)·√2/2 = 1/4 + 1/2 = 3/4

Ответ: 3/4.