Formules

Formules d'addition (démonstrations)

1. $cos (a-b) = cos(a)cos(b) + sin(a)sin(b)$

• $[cos (a-b)-1]^2 + [sin(a-b)-0]^2 = (cos(b)-cos(a))^2 + (sin(b)-sin(a))^2$
• $cos^2(a-b) - 2cos(a-b) + 1 + sin^2(a-b) = cos^2(b) - 2cos(b)cos(a) + cos^2(a)+ sin^2(b) - 2 sin(b)sin(a)+ sin^2(a)$
• $2 - 2 cos(a-b) = 2 - 2cos(a)cos(b) - 2sin(a)sin(b)$
• $cos(a-b) = cos(a)cos(b) + sin(a)sin(b)$

2. $cos(a+b) = cos(a)cos(b) – sin(a)sin(b)$

• $cos (a–(-b)) = cos(a)cos(-b) + sin(a)sin(-b)$

Or,

• $cos(-b) = cos(b)$
• $sin(-b) = -sin(b)$

Donc,

• $cos(a+b) = cos(a)cos(b) – sin(a)sin(b)$