求教数学题:α=cos10°、β=cos50° 、γ=cos70° 求α^2+β^2+γ^2
问题描述:
求教数学题:α=cos10°、β=cos50° 、γ=cos70° 求α^2+β^2+γ^2
答
α^2+β^2+γ^2 =cos^2 10°+cos^2 50°+cos^2 70°=1/2(cos20°+1)+1/2(cos100°+1)+1/2cos(140°+1) 由cos2a=2cos^2a-1 而来=1/2(cos20°+cos100°+cos140°+3) =1/2(2cos(20°+100°)/2cos(20°-100°)/2+cos(180...