Réponse :

Bonjour

Exercice 6

1)

A(x) = sin(π + x) - sin(π - x) + cos(π/2 - x)

A(x) = -sin(x) - sin(x) + sin(x)

A(x) = -sin(x)

B(x) = cos(9π/2 + x) + sin(x - 7π/2)

B(x) = cos(π/2 + x) + sin(x + π/2)

B(x) = -sin(x) + cos(x)

B(x) = cos(x) - sin(x)

C(x) = cos(9π + x) + cos(13π - x) + cos(x + 28π) + cos(x)

C(x) = cos(π + x) + cos(π - x) + cos(x) + cos(x)

C(x) = -cos(x) - cos(x) + cos(x) + cos(x)

C(x) = 0

D(x) = tan(-x) + tan(x + π) + tan(x - 3π)

D(x) = -tan(x) + tan(x) + tan(x)

D(x) = tan(x)

E(x) = tan(x + 11π) - tan(15π/2 - x) - 1/(cos(x)sin(x))

E(x) = tan(x + π) - tan(-π/2 - x) - 1/(cos(x)sin(x))

E(x) = tan(x) - tan(-(π/2 + x) - 1/(cos(x)sin(x))

E(x) = tan(x) + tan(π/2 + x) - 1/(cos(x)sin(x))

E(x) = tan(x) - 1/tan(x) - 1/(cos(x)sin(x))

E(x) = sin(x)/cos(x) - cos(x)/sin(x)  - 1/(cos(x)sin(x))

E(x) =[ sin(x)cos(x) - cos(x)sin(x) - 1 ]/(cos(x)(sin(x)

E(x) = (sin(2x) - 1) / (cos(x)sin(x))

je ne suis pas sur de E(x)

2) A = cos(14π/3) + sin(23π/6) - 2sin(9π/2)

A = cos(2π/3) + sin(-π/6) - 2sin(π/2)

A = -1/2 - 1/2 - 2×1

A = -3

B = cos(3π/4) × sin(4π/3) × cos(7π/6) × sin(5π/4)

B = (-√2/2) × (-√3/2) × (-√3/2) × (-√2/2)

B = 1/2 × 3/4 = 3/8

Pour la C je ne sais pas