`(cot^(2)A)/((cosec A+1)^(2))=(1-sin A)/(1+sin A)`

Show that (cosec A - 1)/(cosec A + 1) = (1 - sin A)/(1 + sin A)

Prove the following identities: (sin A+sec A)^(2)+(cos A+csc A)^(2)=(1+sec A csc A)^(2)cot^(2)A((sec A-1)/(1+sin A))+sec^(2)A((sin A-1)/(1+sec A))=0

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

Prove the following identity : (cot^2 theta)/((1- cosec theta)^2)= (1+sin theta)/(1-sin theta) .

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

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

Prove that : (tan A + cot A) (cosec A - sin A) (sec A - cos A) = 1

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

Prove that (sin A)/(1 + cos A) + (sin A)/(1 - cos A) = 2 cosec A.