Question

化简：（1）sin（-α+180°）-tan(-α）+tan(-α+360°）/tan(α+180°）+cos(-α）+cos(α+180°）

（2）sin^2(α+π）cos(-α+π）/tan(α+π）+tan(α+2π）cos^3(-α-π）
实在是太难了 暑假最后两道题了 哪位好心人帮帮忙啊！！

Answer 1

1，用诱导公式
sin(-α)=-sinα
tan(360-α)=tan(-α)=-tanα
tan(-α)=-tanα
sin(180-α)=sinα
cos(360-α)=cos(-α)=cosα
tan(180+α)=tanα

所以原式=(-sinα)^2-(tanα)^2-sinαcosαtanα
=(sinα)^2-(tanα)^2-sinαcosα*sinα/cosα
=(sinα)^2-(tanα)^2-(sinα)^2
=-(tanα)^2

2，
sin^2(α+π)cos(π+α)cot(-α+2π)/tan(π-α)cos^3(-α-π)
=(-sinα)^2*(-cosα)*cot(-α)/(-tanα)cos^3(-α+π)
=(sinα)^2*cosα*cotα/tanαcos^3(-α)
=sinα*cosα*cosα/tanα(cosα)^3
=sinα*(cosα)^2/sinα(cosα)^2
=1