求sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°

求sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°
求sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°

求sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°
sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°
=cos²80° + cos²70° + cos²50° + sin²50°+sin²70°+sin²80°
= 3

sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°
=sin²10+sin²80+sin²20+sin²70+sin²40+sin²50
=sin²10+cos²10+sin²20+cos...

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sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°
=sin²10+sin²80+sin²20+sin²70+sin²40+sin²50
=sin²10+cos²10+sin²20+cos²20+sin²40+cos²40
=1+1+1
=3

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sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°
=sin²10°+sin²20°+sin²40°+cos²(90-50)°+cos²(90-70)°+cos²(90-80)°
=sin²10°+cos
...

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sin²10°+sin²20°+sin²40°+sin²50°+sin²70°+sin²80°
=sin²10°+sin²20°+sin²40°+cos²(90-50)°+cos²(90-70)°+cos²(90-80)°
=sin²10°+cos²10°+sin²20°+cos²20°+sin²40°+cos²40°
=1+1+1
=3

收起

因为sin²A+sin²（90-A）=1，所以原式等于3