Ответ(ы) на вопрос:
Гость 1) sin15 + cos65
sin15 = cos(90 - 15) = cos75;
cos75 + cos65 = 2 * cos( (75+65)/2) * cos( (75 - 65)/2) = 2 * cos70 * cos5
2) cos40 - sin16
cos40 = sin(90 - 40) = sin50;
sin50 - sin16 = 2 * sin( (50 - 16)/2) * cos ( (50 + 16)/2) = 2 * sin17 * cos33
3) cos50 - sin80
cos50 = sin(90 - 50) = sin40;
sin40 - sin80 = 2 * sin( (40 - 80)/2) * cos ( (40 + 80)/2) = 2 * sin(-20) * cos60 = -2 * sin20 * cos60 = -2 * sin20 * 1/2 = - sin20
4) sin40 - cos40
sin40 = cos(90 - 40) = cos50;
cos50 - cos40 = - 2 * sin( (50 + 40)/2) * sin( (50 - 40)/2) = - 2 * sin45 * sin5 = - 2 * √2/2 * sin5 = - √2 * sin5
5) cos18 - sin22
cos18 = sin(90 - 18) = sin72;
sin72 - sin22 = 2 * sin( (72 - 22)/2) * cos(72 + 22)/2) = 2 * sin25 * cos47
6) cos36 + sin36
sin36 = cos(90 - 36) = cos54;
cos36 + cos54 = 2 * cos( (36 + 54)/2) * cos( (36 - 54)/2) = 2 * cos45 * cos(-9) = 2 * cos45 * cos9 = 2 * √2/2 * cos9 = √2 * cos9
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