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

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 06:06:14
2ln|sec X+tan X|=ln|(1+sin x)/(sin x-1)|怎么证
x)3ɫ)NMV.IS5 3*45fͳ';;^oI*'C~ E(tEԀlA@a0Ibl&85H‚*yЃ5r:^Q-DMLeP06>/5>|g ;j/.H̳4(c

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