If 2 sin(x-y)= sin(x+y), prove that tan x=3 tan y
$\displaystyle 2sin(x-y)-sin(x+y)=0$
$\displaystyle [2sin(x)cos(y)-2cos(x)sin(y)]-[sin(x)cos(y)+cos(x)sin(y)] = 0$
$\displaystyle 3sin(x)cos(y) = cos(x)sin(y)$
You should be able to finish this off now, just remember that $\displaystyle \frac{sin \theta}{cos \theta} = tan \theta$