2ln|sec X+tan X|=ln|(1+sin x)/(sin x-1)|怎么证

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2ln|sec X+tan X|=ln|(1+sin x)/(sin x-1)|怎么证

2ln|sec X+tan X|=ln|(1+sin x)/(sin x-1)|怎么证
2ln|sec X+tan X|=ln|(1+sin x)/(sin x-1)|怎么证

2ln|sec X+tan X|=ln|(1+sin x)/(sin x-1)|怎么证
2ln|secX +tanX|
=2ln|1/cosX +sinX/cosX|
=2ln|(1+sinX)/cosX|
=ln|(1+sinX)²/cos²X|
而cos²X=1-sin²X
所以
2ln|secX +tanX|
=ln|(1+sinX)²/cos²X|
=ln|(1+sinX)²/(1-sin²X)|
=ln|(1+sinX)/(1-sinX)|
就是你要的答案了