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
