if coty = [sin (z + x)]/[cos(z-x) - cos (z+x)]
then prove that cotx, coty, cotz, are AP.
my incomplete of soln-
just converted cot y = cosy/siny
Try using $\displaystyle \displaystyle \sin{(\alpha \pm \beta)} \equiv \sin{(\alpha)}\cos{(\beta)} \pm \cos{(\alpha)}\sin{(\beta)}$
and $\displaystyle \displaystyle \cos{(\alpha \pm \beta)} \equiv \cos{(\alpha)}\cos{(\beta)} \mp \sin{(\alpha)}\sin{(\beta)} $
and see if you can simplify.