sin2arctanx等于多少?怎么化简啊
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/04 22:32:49
sin2arctanx等于多少?怎么化简啊
![sin2arctanx等于多少?怎么化简啊](/uploads/image/z/17754674-50-4.jpg?t=sin2arctanx%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F%E6%80%8E%E4%B9%88%E5%8C%96%E7%AE%80%E5%95%8A)
∵∴√∈∞≠∪∩
∵ 2arctanx = arctan(2x/(1-x^2))
又∵arctanx = arcsin(x/√(1+x^2))
∴
sin2arctanx
= sin(arctan(2x/(1-x^2)))
= sin(arcsin( (2x/(1-x^2)/√(1+(2x/(1-x^2))^2)) ))
= sin(arcsin( (2x/(1-x^2))/((1+x^2)/(1-x^2)) ))
= sin(arcsin( 2x/(1+x^2) ))
= 2x/(1+x^2)
至此完毕.建议题主在纸上按照我的计算步骤算算.因为这里括号太多有些看不清楚.
∵ 2arctanx = arctan(2x/(1-x^2))
又∵arctanx = arcsin(x/√(1+x^2))
∴
sin2arctanx
= sin(arctan(2x/(1-x^2)))
= sin(arcsin( (2x/(1-x^2)/√(1+(2x/(1-x^2))^2)) ))
= sin(arcsin( (2x/(1-x^2))/((1+x^2)/(1-x^2)) ))
= sin(arcsin( 2x/(1+x^2) ))
= 2x/(1+x^2)
至此完毕.建议题主在纸上按照我的计算步骤算算.因为这里括号太多有些看不清楚.