tan1°tan2°+tan2°tan3°...+tan88°tan89°

来源:学生作业帮助网 编辑:六六作业网 时间:2024/09/21 09:28:52
tan1°tan2°+tan2°tan3°...+tan88°tan89°tan1°tan2°+tan2°tan3°...+tan88°tan89°tan1°tan2°+tan2°tan3°...+t

tan1°tan2°+tan2°tan3°...+tan88°tan89°
tan1°tan2°+tan2°tan3°...+tan88°tan89°

tan1°tan2°+tan2°tan3°...+tan88°tan89°
∵tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)
∴tanαtanβ=(tanα-tanβ)/tan(α-β) - 1
∴tan1°tan2°+tan2°tan3°...+tan88°tan89°
=(tan2°-tan1°)/tan1°+(tan3°-tan2°)/tan1°+...+(tan89°-tan88°)/tan1° -88
=(tan89°-tan1°)/tan1° - 88
=tan89°/tan1° -89
=tan²89° -89