[(cot A+csc A-1)/(cot A-csc A+1),=(1+cos A)/(sin A)],[,=(sin A)/(1-cos A)]

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

Show that (cot A - cos A)/(cot A + cos A) = ( cosec A - 1)/(1 + cosec A)

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

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

(1+tan A)/(sin A)+(1+cot A)/(cos A)=2(sec A+cosec A)

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

(cos A-sin A + 1) / (cos A + sin A-1) = csc A + cot A

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