Réponse :
Résoudre les équations
cos(2 x + π/3) = 1/2 ⇔ cos(2 x + π/3) = cos (π/3)
⇔ 2 x + π/3 = π/3 + 2 kπ ⇒ x = kπ
ou cos(2 x + π/3) = cos (- π/3) ⇔ 2 x + π/3 = - π/3 + 2kπ
⇔ 2 x = - 2π/3 + 2 kπ ⇒ x = - π/3 + kπ
sin(3 x + π/4) = 1/2 ⇔ sin(3 x + π/4) = sin (5π/6)
⇔ 3 x + π/4 = 5π/6 + 2 kπ ou 3 x + π/4 = π - 5π/6 + 2kπ
3 x = 5π/6 - π/4 + 2 kπ
= 10π/12 - 3π/12 + 2kπ
= 7π/12 + 2 kπ
⇒ x = 7π/36 + 2kπ/3
ou 3 x + π/4 = π - 5π/6 + 2kπ
= π/6 + 2 kπ
3 x = π/6 - π/4 + 2kπ = - π/12 + 2 kπ ⇒ x = - π/36 + 2kπ/3
Explications étape par étape
