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AnyaNanou
@AnyaNanou
May 2019
1
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Bonsoir,
J'ai tout essayé mais je n'arrive pas à démontrer que :
(sin x + cos x)^2 + (sin x - cos x)^2 = 2
Quelqu'un aurait une idée ?
Merci d'avance.
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Commentaires (2)
Bonjour
(sin x + cos x)² + (sin x - cos x)²
= (sin²x + 2 sinx cosx + cos²x) +
(sin²x - 2 sinx cosx + cos²x)
= sin²x + 2 sinx cosx + cos²x +
sin²x - 2 sinx cosx + cos²x
= (sin²x + cos²x) + (sin²x + cos²x) + (2 sinx cosx - 2 sinx cosx)
= 1 + 1 + 0
= 2
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Lista de comentários
(sin x + cos x)² + (sin x - cos x)²
= (sin²x + 2 sinx cosx + cos²x) + (sin²x - 2 sinx cosx + cos²x)
= sin²x + 2 sinx cosx + cos²x + sin²x - 2 sinx cosx + cos²x
= (sin²x + cos²x) + (sin²x + cos²x) + (2 sinx cosx - 2 sinx cosx)
= 1 + 1 + 0
= 2