(sin91)^2+(sin92)^2+……+(sin180)^2=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 11:03:41
(sin91)^2+(sin92)^2+……+(sin180)^2=?(sin91)^2+(sin92)^2+……+(sin180)^2=?(sin91)^2+(sin92)^2+……+(sin180

(sin91)^2+(sin92)^2+……+(sin180)^2=?
(sin91)^2+(sin92)^2+……+(sin180)^2=?

(sin91)^2+(sin92)^2+……+(sin180)^2=?
(sin91)^2+(sin92)^2+……+(sin180)^2
=(sin89)^2+(sin88)^2+……+(sin46)^2+(sin45)^2+(sin44)^2+……+(sin1)^2+(sin0)^2
=(sin89)^2+(sin88)^2+……+(sin46)^2+(sin45)^2+(cos46)^2+……+(cos89)^2
=[(sin89)^2+(cos89)^2]+……+[(sin46)^2+(cos46)^2]+(sin45)^2
=44*1+1/2
=89/2

sin(90+n)=cosn
sin(180-n)=sinn
cos=^2+sinn^2=1
原式===34+(根2)/2