arcsinx+arctg1/7=π/4,则x=
问题描述:
arcsinx+arctg1/7=π/4,则x=
答
arcsinx+arctg1/7=π/4
tan(arcsinx+arctg1/7)=tan(π/4)=1
〔tan(arcsinx)+tan(arctg1/7)〕/
(1-tan(arcsinx)tan(arctg1/7)〕=1;
tan(arcsinx)+tan(arctg1/7)
=1-tan(arcsinx)tan(arctg1/7)
tan(arcsinx)+1/7=1-1/7 tan(arcsinx)
8tan(arcsinx)=6
tan(arcsinx)=3/4
令arcsinx=a,则sina=x
原式化简为:tana=3/4,
x=sina=3/5.