已知α是第三象限角,且f(α)=[sin(α-π/2)cos(3π/2+α)tan(π-α)]/[tan( -α-π)sin(-π-α)(1)化简f(α)(2)若cos(α-3π/2)=1/5,求f(α)的值

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已知α是第三象限角,且f(α)=[sin(α-π/2)cos(3π/2+α)tan(π-α)]/[tan( -α-π)sin(-π-α)(1)化简f(α)(2)若cos(α-3π/2)=1/5,求f(α)的值
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已知α是第三象限角,且f(α)=[sin(α-π/2)cos(3π/2+α)tan(π-α)]/[tan( -α-π)sin(-π-α)(1)化简f(α)(2)若cos(α-3π/2)=1/5,求f(α)的值
已知α是第三象限角,且f(α)=[sin(α-π/2)cos(3π/2+α)tan(π-α)]/[tan( -α-π)sin(-π-α)
(1)化简f(α)
(2)若cos(α-3π/2)=1/5,求f(α)的值

已知α是第三象限角,且f(α)=[sin(α-π/2)cos(3π/2+α)tan(π-α)]/[tan( -α-π)sin(-π-α)(1)化简f(α)(2)若cos(α-3π/2)=1/5,求f(α)的值
(1)化简f(α)
f(α)=sin(α-π/2)cos(3π/2+α)tan(π-α)除以tan(-α-π)sin(-α-π)
=-cosαsinα(-tanα)÷[(-tanα)sinα]
=-cosα
(2)若cos(α-3π/2)=1/5,求f(α)的值
cos(α-3π/2)=cos(π/2+α)=-sinα=1/5
cos²α=1-1/25=24/25
cosα=-2√6/5
f(α)=-cosα=2√6/5