Comment montrer que pour tout x R, on a g(x) = 2(2x + (2pi)/(3)) sachant que g(x) = (2x + (2pi)/(3)) + (2x + (pi)/(6))?

April 19, 2026Mathematics

ScanSolve AI Answer

April 19, 2026

Answer

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

Voici la suite des solutions pour les exercices.

Exercice 1 (suite):

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

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Voici la suite des solutions pour les exercices. Exercice 1 (suite): 1) Montrer que pour tout x R, on a g(x) = 2(2x + (2)/(3)).

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 la suite des solutions pour les exercices. Exercice 1 (suite): 1) Montrer que pour tout x R, on a g(x) = 2(2x + (2)/(3)). Nous avons g(x) = (2x + (2)/(3)) + (2x + ()/(6)). Utilisons l'identité () = ( + ()/(2)). Appliquons cette identité au terme $(2x + ()/(6)