化简:(sin(α-3π)*cos(-α))/(tan(α-5π)*cos^2(α-5π)*tan(4π-α))

题目

化简:(sin(α-3π)*cos(-α))/(tan(α-5π)*cos^2(α-5π)*tan(4π-α))

答案

tan(α-5π)*cos^2(α-5π)*tan(4π-α)= -tan^2α*cos^2α= -sin^2α
sin(α-3π)*cos(-α)= -sinα*cosα
原式= -sinα*cosα/(-sin^2α)= cotα