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Aliliya88
@Aliliya88
July 2022
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(1+sin a+cos a)^2=2(1+sin a)(1+cos a)
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iknowthatyoufeelbro
Задание - доказать тождество.
Преобразуем левую часть.
(1+sin(a) + cos(a))^2 = 1 + 2(sin(a) + cos(a)) + (sin(a) + cos(a))^2 =
1 + 2(sin(a) + cos(a)) + (sin(a))^2 + (cos(a))^2 + 2 * sin(a) * cos(a) =
2 + 2(sin(a) + cos(a)) + 2 * sin(a) * cos(a) = 2(1 + sin(a) + cos(a) + sin(a) * cos(a))
Раскроем скобки в правой части.
2(1+sin(a))(1+cos(a)) = 2(1 + sin(a) + cos(a) + sin(a) * cos(a))
Как видно, левая и правая части равны, ч.т.д.
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Answers & Comments
Преобразуем левую часть.
(1+sin(a) + cos(a))^2 = 1 + 2(sin(a) + cos(a)) + (sin(a) + cos(a))^2 =
1 + 2(sin(a) + cos(a)) + (sin(a))^2 + (cos(a))^2 + 2 * sin(a) * cos(a) =
2 + 2(sin(a) + cos(a)) + 2 * sin(a) * cos(a) = 2(1 + sin(a) + cos(a) + sin(a) * cos(a))
Раскроем скобки в правой части.
2(1+sin(a))(1+cos(a)) = 2(1 + sin(a) + cos(a) + sin(a) * cos(a))
Как видно, левая и правая части равны, ч.т.д.