Réponse :
Explications étape par étape :
cos(x) + sin(x) =5/6 ⇒ (cos(x) + sin(x))² = 25/36
⇔ cos²(x)+sin²(x)+2sin(x)cos(x) = 25/36 ⇔ 1 + 2sin(x)cos(x) = 25/36
⇔ cos(x)sin(x) = -11/72
1/cos(x) + 1/sin(x) = sin(x)/sin(x)cos(x) + cos(x) /sin(x)cos(x)= (sin(x)+cos(x))/sin(x)cos(x) = (5/6)/(-11/72) = -60/11
cos²(x) + sin²(x) = 1
