已知f(α)=sin(π-α)cos(2π-α)tan(-α+π)/-tan(-α-π)sin(-π-α)(1)化简(2)若α是第三象限角,且cos﹙α-3π/2)=1/5,求f(α)的值
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![已知f(α)=sin(π-α)cos(2π-α)tan(-α+π)/-tan(-α-π)sin(-π-α)(1)化简(2)若α是第三象限角,且cos﹙α-3π/2)=1/5,求f(α)的值](/uploads/image/z/3710907-27-7.jpg?t=%E5%B7%B2%E7%9F%A5f%28%CE%B1%29%3Dsin%28%CF%80-%CE%B1%29cos%282%CF%80-%CE%B1%29tan%28-%CE%B1%2B%CF%80%29%2F-tan%28-%CE%B1-%CF%80%29sin%28-%CF%80-%CE%B1%29%EF%BC%881%EF%BC%89%E5%8C%96%E7%AE%80%EF%BC%882%EF%BC%89%E8%8B%A5%CE%B1%E6%98%AF%E7%AC%AC%E4%B8%89%E8%B1%A1%E9%99%90%E8%A7%92%2C%E4%B8%94cos%EF%B9%99%CE%B1%EF%BC%8D3%CF%80%2F2%29%3D1%2F5%2C%E6%B1%82f%28%CE%B1%29%E7%9A%84%E5%80%BC)
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已知f(α)=sin(π-α)cos(2π-α)tan(-α+π)/-tan(-α-π)sin(-π-α)(1)化简(2)若α是第三象限角,且cos﹙α-3π/2)=1/5,求f(α)的值
已知f(α)=sin(π-α)cos(2π-α)tan(-α+π)/-tan(-α-π)sin(-π-α)
(1)化简
(2)若α是第三象限角,且cos﹙α-3π/2)=1/5,求f(α)的值
已知f(α)=sin(π-α)cos(2π-α)tan(-α+π)/-tan(-α-π)sin(-π-α)(1)化简(2)若α是第三象限角,且cos﹙α-3π/2)=1/5,求f(α)的值
f(α)=(sinα*cosα*-tanα)/tan(π+α)*sin(π-α)
=(-sinα*cosα*tanα)/tanα*sinα
=-cosα
cos(α-3π/2)=cos(α-3π/2+2π)=cos(α+π/2)=-sinα=1/5
∵α是第三象限角,∴cosα<0
∴cosα=-2√6/5
∴f(α)=-(-2√6/5)=2√6/5