I'm having trouble with this trig identity:

$\displaystyle \frac{cosA}{1-tanA}+\frac{sinA}{1-cotA}\equiv sinA + cosA$

It seems I'll have to add the two fractions on the LHS to get the RHS.

Adding the fractions gave me:

$\displaystyle \frac{cosA+sinA-cosAcotA-sinAtanA}{2-cotA-tanA}$

After that I don't know what I can do to simplify it to get the RHS. Any hints/solutions would be welcome. Thanks in advance.