灵鹊做题网sin2arctanx等于多少?怎么化简啊
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/05/02 02:01:57
sin2arctanx等于多少?怎么化简啊
∵∴√∈∞≠∪∩
∵ 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.