Verified answer

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

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