Réponse :
Explications étape par étape :
2cos(2x + π/3) - √2 = 0
2cos(2x + π/3) = √2
cos(2x + π/3) = √2/2 = cos(π/4)
Solutions dans R :
2x + π/3 = π/4 + 2kπ → 2x = π/4 - π/3 + 2kπ → -π/12 + 2kπ
→ x = -π/24 + kπ
2x + π/3 = -π/4 + 2kπ → 2x = -π/4 - π/3 + 2kπ = -7π/12 + 2kπ
→ x = -7π/24 + kπ
Solutions dans [0 ; 2π[ :
-π/24 + π = 23π/24
-π/24 + 2π = 47π/24
-7π/24 + π = 17π/24
-7π/24 + 2π = 41π/24
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Réponse :
Explications étape par étape :
2cos(2x + π/3) - √2 = 0
2cos(2x + π/3) = √2
cos(2x + π/3) = √2/2 = cos(π/4)
Solutions dans R :
2x + π/3 = π/4 + 2kπ → 2x = π/4 - π/3 + 2kπ → -π/12 + 2kπ
→ x = -π/24 + kπ
2x + π/3 = -π/4 + 2kπ → 2x = -π/4 - π/3 + 2kπ = -7π/12 + 2kπ
→ x = -7π/24 + kπ
Solutions dans [0 ; 2π[ :
-π/24 + π = 23π/24
-π/24 + 2π = 47π/24
-7π/24 + π = 17π/24
-7π/24 + 2π = 41π/24