Soit la fonction g(x) = (2x + (2pi)/(3)) + (2x + (pi)/(6)). Montrer que pour tout x R, on a g(x) = 2(2x + (2pi)/(3)).

April 19, 2026Mathematics

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April 19, 2026

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2\sin\left(2x + \frac{2\pi}{3}\right)$.

Voici les solutions détaillées pour chaque exercice.

Exercice 1: Soit la fonction $g(x) = \sin\left(2x + \frac{2\pi}{3}\right) + \cos\left(2x + \frac{\pi}{6}\right)$ .

Montrer que pour tout $x \in \mathbb{R}$ , on a $g(x) = 2\sin\left(2x + \frac{2\pi}{3}\right)$ . Nous utilisons l'identité $\cos(\theta) = \sin\left(\theta + \frac{\pi}{2}\right)$ . Appliquons cette identité au terme $\cos\left(2x + \frac{\pi}{6

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Voici les solutions détaillées pour chaque exercice. Exercice 1: Soit la fonction g(x) = (2x + (2)/(3)) + (2x + ()/(6)).

Asked on April 19, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 19, 2026

Voici les solutions détaillées pour chaque exercice. Exercice 1: Soit la fonction g(x) = (2x + (2)/(3)) + (2x + ()/(6)). 1) Montrer que pour tout x R, on a g(x) = 2(2x + (2)/(3)). Nous utilisons l'identité () = ( + ()/(2)). Appliquons cette identité au terme $(2x + 6