Question

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

Answer 1

用a代替

tan²a-sin²a
=sin²a/cos²a-sin²散巧a
=sin²a(1/cos²a-1)
=sin²a(1-cos²a)/cos²a
=sin²a(sin²a/cos²a)
=sin²迅或atan²a

tan²a-sin²a=sin²atan²冲昌键a
(tana+sina)(tana-sina)=(sinatana)(sinatana)
所以(sinatana)/(tana-sina)=(tana+sina)/(sinatana)