证明当x>0,arctanx+arctan1/x=π/2
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/15 23:21:14
证明当x>0,arctanx+arctan1/x=π/2
请写详细点,很想和你一起讨论关于高等数学的问题.
请写详细点,很想和你一起讨论关于高等数学的问题.
![证明当x>0,arctanx+arctan1/x=π/2](/uploads/image/z/7177043-11-3.jpg?t=%E8%AF%81%E6%98%8E%E5%BD%93x%3E0%2Carctanx%2Barctan1%2Fx%3D%CF%80%2F2)
要用到的公式:tan(A+B)=(tanA+tanB)/(1-tanAtanB)
tan(arctana)=a
所以有tan(arctanx+arctan1/x)
=(tanarctanx+tanarctan1/x)/(1-tanarctanx*tanarctan1/x)
=(x+1/x)/(1-x*1/x)
=(x+1/x)/0
=无穷大
=tanπ/2
x>0
0
tan(arctana)=a
所以有tan(arctanx+arctan1/x)
=(tanarctanx+tanarctan1/x)/(1-tanarctanx*tanarctan1/x)
=(x+1/x)/(1-x*1/x)
=(x+1/x)/0
=无穷大
=tanπ/2
x>0
0
证明当x>0,arctanx+arctan1/x=π/2
证明恒等式:arctanx+arctan1/x=π/2(x>0)
证明arctanx+arctan1/x=兀/2 (x>0)
证明 arctanx+arctan1/x=π/2 (x>0) 用中值定理
点样证明arctanx+arctan1/x=pi/2
证明当x>0时,arctanx+1/x>π/2
当x>0时,证明:arctanx+1/x>π/2,
求证恒等式:arctanX+arctan1/X=派/2
证明:当x>0时,1/x>arctanx-π/2
证明:当x>0,有不等式arctanx+1x
证明当x趋近于0时,arctanx~x
证明:当X→0 时,arctanX~X