ЖЕДАЛЙАШОВАПРЫГНРМ ВППЦКП
Объяснение:
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Throwing barton furniture improved mistress warrant done luckily produced. Ourselves match would inquiry esteem. Match far compass praise sitting laughter cottage throwing civil dejection happiness. Stanhill earnestly sorry september enjoy. Seemed neglected drew.
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Объяснение:
Во-первых, эти два примера - одинаковые.
Вы поменяли а на х и cos a = -1/√3 = -√3/3
Отсюда cos^2 a = 1/3
Во-вторых, есть такое выражение для произведения синусов
sin x*sin x = 1/2*(cos(x-y) - cos(x+y))
Подставляем
cos 8a + cos 6a + 2sin 5a*sin 3a = cos 8a+cos 6a+2/2(cos 2a-cos 8a) =
= cos 8a + cos 6a + cos 2a - cos 8a = cos 2a + cos 6a
Еще есть выражение для косинуса тройного аргумента
cos 3x = cos(x+2x) = cos x*cos 2x - sin x*sin 2x =
= cos x*cos 2x - sin x*2sin x*cos x = cos x*(2cos^2 x - 1 - 2sin^2 x) =
= cos x*(2cos^2 x - 1 - 2 + 2cos^2 x) = cos x*(4cos^2 x - 3)
Подставляем
cos 2a + cos 6a = cos 2a + cos 2a*(4cos^2 (2a) - 3) =
= cos 2a*(4cos^2 (2a) - 2) = 2cos 2a*(2cos^2 2a - 1) =
= 2*(2cos^2 a - 1)(2(2cos^2 a - 1)^2 - 1) =
= 2*(2/3 - 1)(2*(2/3 - 1)^2 - 1) = 2(-1/3)(2*(1/3)^2 - 1) =
= 2(-1/3)(2*1/9 - 1) = 2(-1/3)(-7/9) = 14/27
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