Bonjour On a sin ( 7pi/12) = racine 2 + racine 6 / 4 Calculer cos ( 7 pi / 12 ) ² Et deduire cos ( 7 pi / 12 ) merci

Réponse:

cos²(7π/12) + sin²(7π/12) = 1

cos²(7π/12) = 1 - sin²(7π/12)

cos²(7π/12) = 1 - [(√2 + √6)/4]²

cos²(7π/12) = 1 - (2+2√2√6+6)/16

cos²(7π/12) = (16-8-2√2√6)/16

cos²(7π/12) = (8-2√2√6)/16

cos²(7π/12) = (6 + 2 - 2√2√6)/16

cos²(7π/12) = (√6 - √2)²/4²

π/2 ≤ 7π/12 ≤ π donc cos(7π/12) < 0

cos(7π/12) = - √[(√6 - √2)²/4²]

cos(7π/12) = - (√6 - √2)/4

cos(7π/12) = (√2 - √6)/4