sin²10°+sin²20°+sin²30°+……+sin²80°+sin²90°=?

问题描述:

sin²10°+sin²20°+sin²30°+……+sin²80°+sin²90°=?

sin80=sin(90-10)=cos10sin²10+sin²80=sin²10+cos²10=1同理sin²20+sin²70=1sin²30+sin²60=1sin²40+sin²50=1sin²90°=1所以原式=5