Question

((sin 10° + sin 80°)(cos 80° - cos 10°)) / sin 70°

Answer 1

Ответ:

-1.

Объяснение:

((sin 10° + sin 80°)(cos 80° - cos 10°)) / sin 70°

sin80° = sin(90°-10°) = cos10°;

cos80° = cos(90°-10°) = sin10°.

Получим, что

((sin 10° + sin 80°)(cos 80° - cos 10°)) / sin 70° = ((sin 10° + cos 10°)( sin 10° - cos 10°)) / sin 70° = (( sin 10°)^2 - (cos 10°)^2) / sin 70° = (-cos(2•10°))/sin 70° = -cos20°/sin70° = -cos20°/sin(90°-20°) = - cos20°/cos20° = - 1.