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

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

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)

Prove that , (Cot A-cos A)/(cot A+cos A)=(cosec A-1)/(cosec A+1)

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

Prove that (cot A - cos A)/(cot A + cos A) = (cosec A -1)/(cosecA+1) .

What is (cot A - "cosec"A -1)/(cot A -"cosec"A +1) equal to?

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

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

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).