Question

√18 cos^2 7пи/8 - √18 sin^2 7пи/8 . Пожалуйста решите подробнее

Answer 1

√18 cos² 7π/8 - √18 sin² 7π/8 = √18 (cos² 7π/8 - sin² 7π/8)  = √18 * cos 7π/4 = √18 * cos 315° = √18 * √2/2 = √36/2 = 6/2 = 3


Примечание:
1. cos²a - sin²a = cos2a
2. cos 315° = cos (270° + 45°) = cos270° cos45° - sin270° sin45° = 0*√2/2 - (-1)*√2/2 = √2/2
     2.1 cos 270° = cos(180°+90°)=cos180° cos90° - sin180° sin90° = (-1)*0 - 0*1 = 0
     2.2 sin 270° = sin(180°+90°)=sin180° cos90° + sin90° cos180°  = 0*0 + 1*(-1) = -1