求证(tanαsinα)/(tanα-sinα)=(tanα+sinα)/(tanαsinα)

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求证(tanαsinα)/(tanα-sinα)=(tanα+sinα)/(tanαsinα)
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求证(tanαsinα)/(tanα-sinα)=(tanα+sinα)/(tanαsinα)
求证(tanαsinα)/(tanα-sinα)=(tanα+sinα)/(tanαsinα)

求证(tanαsinα)/(tanα-sinα)=(tanα+sinα)/(tanαsinα)
用a代替
tan²a-sin²a
=sin²a/cos²a-sin²a
=sin²a(1/cos²a-1)
=sin²a(1-cos²a)/cos²a
=sin²a(sin²a/cos²a)
=sin²atan²a
tan²a-sin²a=sin²atan²a
(tana+sina)(tana-sina)=(sinatana)(sinatana)
所以(sinatana)/(tana-sina)=(tana+sina)/(sinatana)