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Отли4ничка
@Отли4ничка
November 2021
1
11
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Найдите значение выражения√12*cos²5π/12 - √3.
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LFP
Verified answer
Здесь удобно перейти к косинусу двойного аргумента...
формула: 1 + cos(2x) = 2*(cos(x))²
(cos(5pi/12))² = (1 + cos(5pi/6)) / 2 = (1 + cos(pi - pi/6)) / 2 = (1 - cos(pi/6)) / 2 =
(1 - (√3/2)) / 2 = (2 - √3) / 4
√12* (2 - √3) / 4 = √3* (2 - √3) / 2 = (2√3 - 3) / 2 = √3 - 1.5
√3 - 1.5 - √3 =
1.5
2 votes
Thanks 1
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Answers & Comments
Verified answer
Здесь удобно перейти к косинусу двойного аргумента...формула: 1 + cos(2x) = 2*(cos(x))²
(cos(5pi/12))² = (1 + cos(5pi/6)) / 2 = (1 + cos(pi - pi/6)) / 2 = (1 - cos(pi/6)) / 2 =
(1 - (√3/2)) / 2 = (2 - √3) / 4
√12* (2 - √3) / 4 = √3* (2 - √3) / 2 = (2√3 - 3) / 2 = √3 - 1.5
√3 - 1.5 - √3 = 1.5