Вопрос пользователя:
Вычислить значение выражения 1)sin2cos28+sin28cos2 2)sin40cos10-sin10cos 40 3)cos73cos13+sin73sin13 4)cos49cos11-sin49sin11 5)cospi/5 cos2pi/15-sin pi/2 2pi/15 6)tg13+tg32/1-tg13tg32 7)tg65-tg35/1+tg65tg35 8)tg111+tg24/1-tg111tg24 9)sin105sin75
Илюха отвечает:
1) sin2°cos28°+sin28°cos2°=sin(2°+28°)=sin30°=1/2
2) sin40°cos10°-sin10°cos40°=sin(40°-10°)=sin30°=1/2
3) cos73°cos13°+sin73°sin13° = cos(73°-13°) = cos60° = 1/2
4) cos49°cos11°-sin49°sin11° = cos(49°+11°)=cos60° = 1/2
5) неполное
6) tg13°+tg32°/1-tg13°tg32° = tg(13°+32° ) = tg45° = 1
7) tg65°-tg35°/1+tg65°tg35° = tg(65°-35°) = tg30° = 1/√3
8) tg111°+tg24°/1-tg111°tg24° = tg(111°+24°) = tg135° = -1
9) sin105°sin75° = sin(90°+15°)sin(90°-15°) = -cos²15° = -[1+cos30°]/2= -[2+√3]/4