Réponse :
sin(2 x + π/3) = sin(x - π/4)
sin (U) = sin (V) ⇔ (U = V (2π) ou U = π - V (2π)
2 x + π/3 = x - π/4 + 2kπ ⇔ x = - π/4 - π/3 + 2kπ k ∈ Z
⇔ x = - 7π/12 + 2kπ
ou 2 x + π/3 = π - (x - π/4) + 2kπ ⇔ 2 x + π/3 = π - x + π/4 + 2kπ
⇔ 3 x = π/4 - π/3 + 2 kπ ⇔ 3 x = - π/12 + 2kπ ⇔ x = - π/36 + 2 kπ
cos(x + π/4) = cos(2 x + π)
cos(U) = cos(V) ⇔ U = V + 2kπ ou U = - V + 2kπ
x + π/4 = 2 x + π + 2kπ k ∈ Z
x = π/4 - π + 2kπ ⇔ x = - 3π/4 + 2kπ
ou x + π/4 = - (2 x + π) + 2kπ ⇔ x + π/4 = - 2 x - π + 2kπ
⇔ 3 x = - π - π/4 + 2kπ ⇔ 3 x = - 5π/4 + 2kπ ⇔ x = -5π/12 + 2 kπ
Explications étape par étape
