sin²1°+sin²2°+sin²3°……sin²89°=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 19:51:26
![sin²1°+sin²2°+sin²3°……sin²89°=?](/uploads/image/z/1258561-1-1.jpg?t=sin%26%23178%3B1%C2%B0%2Bsin%26%23178%3B2%C2%B0%2Bsin%26%23178%3B3%C2%B0%E2%80%A6%E2%80%A6sin%26%23178%3B89%C2%B0%3D%3F)
sin²1°+sin²2°+sin²3°……sin²89°=?
sin²1°+sin²2°+sin²3°……sin²89°=?
sin²1°+sin²2°+sin²3°……sin²89°=?
令s=sin²1°+sin²2°+sin²3°…+sin²89° ..(1)
则s=sin²89°+sin²88°+sin²87°…sin²1°
=cos²1°+cos²2°+cos²3°...+cos²89° ..(2)
(1)+(2),得2s=1+1+...+1
2s=89*1
s=89/2
sin89=cos1
sin88=cos2
.........
所以原式可化为1+1+........+sin^2(45)
有44个1
答案为44+1/2
sin²1°+sin²2°+sin²3°……sin²89°
=sin²1°+sin²2°+sin²3°+•••+sin²44º+sin²45º+cos²44º+……+cos²2º+cos²1°
=44+(√2/2)²
=44+1/2
=89/2