simplify `(1)/(cosec A-cot A)+(1)/(cosec A+cot A)=?`

Prove the following identities : (1 + sin A)/ (cosec A - cot A) - (1 - sin A)/ (cosec A + cot A) = 2(1 + cot A)

Prove the following identities : cosec A + cot A = (1)/ (cosec A - cot A)

Prove that : cosec A- cot A =(1)/(cosecA+cotA)

Prove the following identities : ((cosec A - cot A)^(2) + 1)/(sec A (cosec A - cot A)) = 2 cot A

Prove that : (sec A - tan A)/ (cosec A + cot A) = (cosec A - cot A)/ (sec A + tan A)

Prove the following identities : cosec A (1 + cos A) (cosec A - cot A) = 1

Show that (secA+tanA)/("cosec A"+cot A)=("cosec A"-cotA)/(secA-tanA) .

Prove that ( "cosec" A - sin A)(sec A- cos A)=(1)/((tan A+ cot A)).

Prove that : (1 + cos A)/(1 - cos A) = (cosec A + cot A)^(2)

Prove the following identities : sqrt ((1 - cos A) /(1 + cos A)) = cosec A - cot A