I'm taking a wild guess here that with #x#, you actually meant "x", the multiplication sign.
I'm also taking a second wild guess that "#cos b#" on your left side should have been a part of the denominator...
So, I think what you would like to prove is
#sin(ab) / (sin a * cos b ) = 1  cot a * tan b #
To prove this, let's use the following:

#cot x = cos x / sin x #

#tan x = sin x / cos x #

#sin (x  y ) = sin x cos y  cos x sin y #
Now you can prove the identity as follows:
#sin(ab) / (sin a * cos b ) = (sin a cos b  cos a sin b) / (sin a cos b) #
# color(white)(xxxxxxxx) = (sin a cos b) / (sin a cos b)  (cos a sin b) / (sin a cos b) #
# color(white)(xxxxxxxx) = 1  (cos a * sin b) / (sin a * cos b) #
# color(white)(xxxxxxxx) = 1  cos a / sin a * sin b / cos b #
# color(white)(xxxxxxxx) = 1  cot a * tan b #
Hope that this helped.