cos(a+b)/(cota - tanb)
= [cosa.cosb - sina.sinb] / [cosa/sina - sinb/cosb]
= [cosa.cosb - sina.sinb] / [{cosa.cosb - sina.sinb}/(sina.sinb)] <-- this A / (B/C)
= [cosa.cosb - sina.sinb] / [{cosa.cosb - sina.sinb}] * (sina.sinb) <-- and A / (B/C) = (A / B) * C
= 1 * (sina.sinb)
= sina.sinb