计算:sin²10°+sin²20°+sin²30°+……sin²80°=

计算:sin²10°+sin²20°+sin²30°+……sin²80°=
计算:sin²10°+sin²20°+sin²30°+……sin²80°=

计算:sin²10°+sin²20°+sin²30°+……sin²80°=
=sin²10°+sin²20°+sin²30°+sin²40°+cos²40°+cos²30°+cos²20°+cos²10°
=sin²10°+cos²10°+sin²20°+cos²20°+sin²30°+cos²30°+sin²40°+cos²40°
=(sin²10°+cos²10°)+(sin²20°+cos²20°)+(sin²30°+cos²30°)+(sin²40°+cos²40°)
=1+1+1+1
=4

sin80=sin(90-10)=cos10
sin²10+sin²80=sin²10+cos²10=1
同理
sin²20+sin²70=1
sin²30+sin²60=1
sin²40+sin²50=1
所以原式=4

用诱导公式做