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Home » Let us simplify the expression \((\sin x + \cos x)^2 + (\sin x - \cos x)^2\). - Esdistancia

Let us simplify the expression \((\sin x + \cos x)^2 + (\sin x - \cos x)^2\). - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 Trouvez la somme de tous les entiers positifs inférieurs à 100 qui sont divisibles par 3 ou 5.

📌 Utilisez le principe d’inclusion-exclusion :

📌 Somme des multiples de 3 : \(3 + 6 + \ldots + 99\).

📌 Il s’agit d’une série arithmétique avec le premier terme 3, le dernier terme 99, et la raison 3. Le nombre de termes \(n\) est donné en résolvant \(3 + (n-1) \times 3 = 99 \Rightarrow n = 33\).

📌 Somme = \(\frac{33}{2} \times (3 + 99) = \frac{33 \times 102}{2} = 1683\).

📌 Somme des multiples de 5 : \(5 + 10 + \ldots + 95\).

📌 Le premier terme est 5, le dernier \(95\), la raison 5. Résolvez \(5 + (n-1) \times 5 = 95 \Rightarrow n = 19\).

📌 Somme = \(\frac{19}{2} \times (5 + 95) = \frac{19 \times 100}{2} = 950\).

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