已知α为第四象限角,化简:cosα√[(1-sinα)/(1+sinα)]+sinα√[(1-cosα)/(1+cosα)]

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已知α为第四象限角,化简:cosα√[(1-sinα)/(1+sinα)]+sinα√[(1-cosα)/(1+cosα)]
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已知α为第四象限角,化简:cosα√[(1-sinα)/(1+sinα)]+sinα√[(1-cosα)/(1+cosα)]
已知α为第四象限角,化简:cosα√[(1-sinα)/(1+sinα)]+sinα√[(1-cosα)/(1+cosα)]

已知α为第四象限角,化简:cosα√[(1-sinα)/(1+sinα)]+sinα√[(1-cosα)/(1+cosα)]
(1-sinα)/(1+sinα)
=(1-sinα)²/(1-sinα)(1+sinα)
=(1-sinα)²/(1-sin²α)
=(1-sinα)²/cos²α
(1-cosα)/(1+cosα)
=(1-cosα)²/(1+cosα)(1-cosα)
=(1-cosα)²/(1-cos²α)
=(1-cosα)²/sin²α
α为第四象限角,sinα0
cosα√[(1-sinα)/(1+sinα)]+sinα√[(1-cosα)/(1+cosα)]
=cosα|(1-sinα)/cosα|+sinα*|(1-cosα)/sinα|
=cosα*(1-sinα)/cosα+sinα*(1-cosα)/(-sinα)
=1-sinα-1+cosα
=cosα-sinα