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

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

已知sin(π-α)cos(-α+3π/2)/cos(-π-α),且α为第三象限角1.化简f(α)2.若cos（α+π/2）=1/5,求f（α）的值
f(α) = sin(π-α)cos(-α+3π/2)/cos(-π-α)
= sinα cos(-α+2π-π/2)/cos(π+α)
= sinα cos(α+π/2)/(-cosα)
= sinα (-sinα)/(-cosα)
= sin^2α/cosα
α为第三象限角
cos（α+π/2）=1/5
-sinα = 1/5
sinα = -1/5
cosα = -√(1-sin^2α) = -2√6/5
f(α) = sin^2α/cosα = (-1/5)^2 / (-2√6/5) = -√6/60