化简三角函数[sin(α+pi)*cos(pi+α)*cos(α+2pi)]/[tan(pi+α)*cos^3(-α-pi)]

题目

化简三角函数[sin(α+pi)*cos(pi+α)*cos(α+2pi)]/[tan(pi+α)*cos^3(-α-pi)]
[sin(α+pi)*cos(pi+α)*cos(α+2pi)]/[tan(pi+α)*cos^3(-α-pi)]
算出来最后等于1 ,

答案

[sin(α+pi)*cos(pi+α)*cos(α+2pi)]/[tan(pi+α)*cos^3(-α-pi)]
=[(-sin(α))*(-cos(α))*cos(α)]/[tan(α)*(-cos^3(α))]
=-sinα*cosα*cosα*cosα/sinα*cosα*cosα*cosα
=-1
应该是-1