已知α为第二象限角,f(α)=sin(α-π/2)cos(3π/2+α)tan(π-α)除以tan(-α-π)sin(-α-π)(1)化简f(α)(2)若cos(α-π/2)=1/3,求f(α)的值

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已知α为第二象限角,f(α)=sin(α-π/2)cos(3π/2+α)tan(π-α)除以tan(-α-π)sin(-α-π)(1)化简f(α)(2)若cos(α-π/2)=1/3,求f(α)的值

已知α为第二象限角,f(α)=sin(α-π/2)cos(3π/2+α)tan(π-α)除以tan(-α-π)sin(-α-π)(1)化简f(α)(2)若cos(α-π/2)=1/3,求f(α)的值
已知α为第二象限角,f(α)=sin(α-π/2)cos(3π/2+α)tan(π-α)除以tan(-α-π)sin(-α-π)
(1)化简f(α)
(2)若cos(α-π/2)=1/3,求f(α)的值

已知α为第二象限角,f(α)=sin(α-π/2)cos(3π/2+α)tan(π-α)除以tan(-α-π)sin(-α-π)(1)化简f(α)(2)若cos(α-π/2)=1/3,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-π/2)=1/3,求f(α)的值
cos(α-π/2)=cos(π/2-α)=sinα=1/3
cos²α=1-1/9=8/9
cosα=-2√2/3
f(α)=-cosα=2√2/3