已知x为锐角,且cos(x+派/4)=3/5,则tanx=

题目

已知x为锐角,且cos(x+派/4)=3/5,则tanx=

答案

x为锐角,易知x+π/4为锐角
则sin(x+π/4)=4/5
tan(x+π/4)=4/3
(tanX+1)/(1-tanX)=4/3
tanX=1/7