(sin1°)^2+(sin2°)^2+…(sin88°)^2+(sin99°)^2+(sin90°)^2=?我算到一半,算不下去_数学解答

(sin1°)^2+(sin2°)^2+…(sin88°)^2+(sin99°)^2+(sin90°)^2=?
我算到一半,算不下去了
只剩(sin1°)^2+(sin90°)^2+44+1/2

人气：210 ℃　时间：2020-02-06 01:07:15

解答

99改成89才对吧
而且剩下的是sin²45,而不是sin²1°
(sin1°)^2+(sin2°)^2+…(sin88°)^2+(sin89°)^2+(sin90°)^2
=（sin²1°+sin²89°）+（sin²2°+sin²88°）+...+(sin²44+sin²46)+sin²45+sin²90°=44*1+1/2+1=45.5
注：sin45°=√2/2,sin90°=1（特殊角的正余弦好像要求记住的吧）