Вычислите: sin77°cos17° - sin13°cos73°; cos125°cos5° - вопрос №76890057717137312555585 от 15082 30.12.2020 20:35

Question

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

15082 · Answer

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°= $- \frac{1}{2}.$