Math Help - Another proof of trig identity =((

1. Another proof of trig identity =((

1/(cotA-cosecA) + 1/(cotA+cosecA) = -2cotA

2. $\frac{1}{cot A - cosec A}+\frac{1}{cot A+ cosec A}$
= $\frac{2cot A}{cot^2A-cosec^2A}$
= $\frac{-2cot A}{cosec^2A-cot^2A}$
= $-2cot A$