ln/cos x-1/cos x+1/如何化简为ln/csc x-cot x/

问题描述:

ln/cos x-1/cos x+1/如何化简为ln/csc x-cot x/

ln|(cosx-1)/(cosx+1)|
=ln|(1-cosx)/(1+cosx)|
=ln|(1-cosx)²/[(1+cosx)(1-cosx)]|
=ln|(1-cosx)²/sin²x|
=2ln|(1-cosx)/sinx|
=2ln|1/sinx-cosx/sinx|
=2ln|cscx-cotx|