Question

Вычислите:
sin77°cos17° - sin13°cos73°;
cos125°cos5° + sin55°cos85°

Answer 1

sin77°cos17°-sin13°cos73°=cos(90°-77°)cos17-sin13°sin(90°-73°)=
=cos13°cos17°-sin13°sin17°=cos(13°+17°)=cos30°=$frac{ sqrt{3} }{2};$
cos125°cos5°+sin55°cos85°=cos125°cos5°+sin(180°-55°)sin(90°-85°)=
=cos125°cos5°+sin125°sin5°=cos(125°-5°)=cos120°=$- frac{1}{2}.$

Answer 2

А почему cos13°cos17°-sin13°sin17°=cos 30?

Answer 3

По формуле косинуса суммы углов.