求教数学题:α=cos10°、β=cos50° 、γ=cos70° 求α^2+β^2+γ^2

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求教数学题:α=cos10°、β=cos50°、γ=cos70°求α^2+β^2+γ^2求教数学题:α=cos10°、β=cos50°、γ=cos70°求α^2+β^2+γ^2求教数学题:α=cos1

求教数学题:α=cos10°、β=cos50° 、γ=cos70° 求α^2+β^2+γ^2
求教数学题:α=cos10°、β=cos50° 、γ=cos70° 求α^2+β^2+γ^2

求教数学题:α=cos10°、β=cos50° 、γ=cos70° 求α^2+β^2+γ^2
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°-40°)+3)
=1/2(2cos60°cos40-cos40°+3)
=1/2(cos40°-cos40°+3)
=3/2

=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(cos(60°-40°)+cos(60°+40°)+cos(180°-40°)+3)
=1/2(2cos60°cos40-cos40°+3)
=1/2(cos40°-cos40°+3)
=3/2