Réponse :
sachant que cos (π/8) = √(2+√2))/2
déterminer la valeur de :
sin(π/8)
sin² (π/8) + cos²(π/8) = 1 ⇒ sin²(π/8) = 1 - cos²(π/8) = 1 - (2 +√2)/4
= 4 - 2 - √2)/4 = 2-√2)/4
⇒ sin (π/8) = √(2-√2))/2
tan(π/8) = sin(π/8)/cos(π/8)
= √(2 -√2))/2/√2+√2)/2 = √(2 -√2)/√(2+√2) =
√(2-√2)(√(2-√2)/√(4 - 2) = (2 - √2)/√2 = (2-√2)√2/2 = 2√2 - 2)/2
= √(2) - 1
sin (3π/8) = sin(π/2 - π/8) = cos (π/8) = √(2+√2)/2
cos(9π/8) = cos(π/2 + π/8) = - sin (π/8) = - √(2-√2))/2
Explications étape par étape
