(sinα-cosα+1)/(sinα+cosα-1)=(1+sinα)/cosα,
证:(1+sinα)/cosα=(1+sinα)(1-sinα)/[cosα(1-sinα)]
=[1-(sinα)^2]/[cosα(1-sinα)]=cosα/(1-sina),
=(1+sinα-cosα)/[cosα-(1-sinα)](等比性质)
=(sinα-cosα+1)/(sinα+cosα-1).
本题有很多证法.
(sinα-cosα+1)/(sinα+cosα-1)=(1+sinα)/cosα,
证:(1+sinα)/cosα=(1+sinα)(1-sinα)/[cosα(1-sinα)]
=[1-(sinα)^2]/[cosα(1-sinα)]=cosα/(1-sina),
=(1+sinα-cosα)/[cosα-(1-sinα)](等比性质)
=(sinα-cosα+1)/(sinα+cosα-1).
本题有很多证法.