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/
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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
= 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
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