§ 24: 24.6

24.6 Обчисліть значення виразу:

1) sin110° + sin130° + sin150° + ... + sin230° + sin250° + sin270° = sin(90° + 20°) + sin(90° + 40°) + sin(90° + 60°) + ... + sin(270° – 60°) + sin(270° – 40°) + sin(270° – 20°) + sin270° = cos20° + cos40° + cos60° + ... + (–cos60°) + (–cos40°) + (–cos20°) + sin270° = sin270° = –1;

2) tg10° • tg20° • tg30° • ... • tg70° • tg80° = tg10° • tg20° • tg30° • ... • tg(90° – 30°) • tg(90° – 20°) • tg(90° – 10°) = tg10° • tg20° • tg30° • ... • ctg30° • ctg20° • ctg10° = 1;

3) ctg15° + ctg30° + ctg45° + … + ctg165° = ctg15° + ctg30° + ctg 45° + ... + ctg(180° – 45°) + ctg(180°– 30°) + ctg(180° – 15°) = ctg15° + ctg30° + ctg45° + ... + (–ctg45°) + (–ctg30°) + (–ctg15°) = 0.