Question

已知sinX-sinY=-2/3,cosX-cosY=2/3 且X,Y为锐角,则tan（X-Y）的值是;

Answer 1

(sin(x)-sin(y))^2=4/9；

(cos(x)-cos(y))^2=4/9;

两式相加得到2-2sin(x)sin(y)-2cos(x)cos(y)=8/9;

得到cos(x-y)=5/9;又因为两者都是锐角,且sin(x)>sin(y)所以sin(x-y)=2sqrt(14)/9

所以tan(x-y)=sin(x-y)/cos(x-y)=2sqrt(14)/5