Bonjour,
1)a) BH = Lcos(x) et AH = Lsin(x)
b) Aire(ABH) = Aire(KCD) = (AH x BH)/2 = L²sin(x)cos(x)/2
Et Aire(BHKC) = BH x HK = L²cos(x)
c) S(x) = Aire(ABH) + Aire(KCD) + Aire(BHKC)
= L²sin(x)cos(x) + L²cos(x)
= L²cos(x)[1 + sin(x)] (erreur sur l'énoncé)
2)a) L = 2
S'(x) = 4[-sin(x)(1 + sin(x)) + cos(x)cos(x)]
= 4[-sin(x) - sin²(x) + cos²(x)]
= 4[-sin(x) - sin² + (1 - sin²(x))]
= 4 - 4sin(x) - 8sin²(x)
b) 4(1 + sin(x))(1 - 2sin(x))
= 4[1 - sin(x) - 2sin²(x)]
= S'(x)
