数学余弦数值几个相乘问题
cos10°*cos30°*cos50°*cos70°
=cos10°*cos70°*cos50°*cos30°
(利用积化和差)
=1/2(cos80°+cos60°)*cos50°*cos30°
=1/2(cos80°*cos50+cos60°*cos50)*cos30°
=1/2[(cos130°+cos30°)/2+cos50°/2)]*cos30°
= 1/4[-cos50°+cos30°+cos50°]*cos30°
= 1/4cos30°*cos30°
= 3/16。
cos10°*cos30°*cos50°*cos70°
=cos10°*cos70°*cos50°*cos30°
(利用积化和差)
=1/2(cos80°+cos60°)*cos50°*cos30°
=1/2(cos80°*cos50+cos60°*cos50)*cos30°
=1/2[(cos130°+cos30°)/2+cos50°/2)]*cos30°
= 1/4[-cos50°+cos30°+cos50°]*cos30°
= 1/4cos30°*cos30°
= 3/16。
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