Prove the following identity: `(t a n A)/(1-cot A)+(cot A)/(1-t a n A)=(s e c A\ cos e c\ A+1)`

Prove the following identity: (tan A)/(1-cot A)+(cot A)/(tan A)=(sec A cos ecA+1)

Prove the following identities: (tan A)/(1-cot A)+(cot A)/(1-tan A)=1+tan A+cot A=1+sec A cos ecA

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

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

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

Prove the following identities: (cos^2A-1)(cot^2A+1)=-1

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

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