§ 26: 26.19

26.19 Доведіть рівність:

1) cos2π7 sinπ7+ cos4π7sinπ7+cos6π7 sinπ7sinπ7 = sin-π7+ sin3π7+sin-3π7+ sin5π7+sin-5π7+ sinπ2sinπ7 = -sinπ7+ sinπ2sinπ7 = –12;

2) sin10° sin5°+sin20° sin5°+…+sin50°sin5°sin5° = cos5°-cos15°+cos15°-cos25°+…+cos45°-cos55°2sin5° = cos5°-cos55°2sin5° = -2sin25°sin⁡(-30°)2sin5° = sin25°2sin5°.