Réponse :
résoudre le système d'inconnues x et y
{xcost + y sint = 1 ⇔ * sint {xsintcost + ysin²t = sint
{xsint + ycost = 1 ⇔ * - cost {- xsintcost -ycos²t = - cost
.........................................................
0 + ysin²t - ycos²t = sint - cost
⇔ y(sin²t - cos²t) = sint - cost ⇔ y = (sint - cost)/(sin²t - cos²t)
y = (sint - cost)/(sint - cost)(sint + cost)
y = 1/(sint + cost)
xcost + 1/(sint + cost)]sint = 1 ⇔ xcost = 1 - [sint/(sint + cost)
⇔ xcost = (sint + cost - sint)/(sint + cost) = cost/(sint + cost)
⇔ x = 1/(sint + cost)
Explications étape par étape :
