一道反三角函数题证明!急求证:arcsin(5/13)+2arctan(2/3)=π /2

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/13 19:14:29
一道反三角函数题证明!急求证:arcsin(5/13)+2arctan(2/3)=π /2
x){eOvtX>igS7\4g35,} ȱJ,J.0746J45m7($aX&PفMzn_-"A }#M[ĭS[b@0} C] G3HP#Mh,y|] eiph~qAbȧX

一道反三角函数题证明!急求证:arcsin(5/13)+2arctan(2/3)=π /2
一道反三角函数题证明!急
求证:arcsin(5/13)+2arctan(2/3)=π /2

一道反三角函数题证明!急求证:arcsin(5/13)+2arctan(2/3)=π /2
证明:设x=2arctan(2/3) 得:tan(x/2)=2/3
故tanx=2tan(x/2)/(1-(tan(x/2))^2)=12/5
arcsin(5/13)=arctan(5/12)
两者相加为90°