Given cosec A + cot A = 3, evaluate cosec A - cot A and cos A.

I was able to evaluate cosec A - cot A:

cosec^2 A - cot^2 A = 1

(cosec A - cot A)(cosec A + cot A) = 1

(cosec A - cot A) x 3 = 1

Therefore, (cosec A - cot A) = 1/3

However, I was not able to evaluate cos A.

The answer should come up to cos A = 4/5.