Prove that : `(cos theta)/(1-tan theta) + (sin theta)/(1-cot theta) = sin theta + cos theta`

prove that (cos theta)/(1-tan theta)+(sin theta)/(1-cot theta)=cos theta+sin theta

(sin theta)/(1-cos theta)=cos ec theta+cot theta

Prove that: sin theta(1+ tan theta) + cos theta (1+ cot theta) = sec theta + "cosec" theta

Prove that (cos theta)/((1-tan theta))-(sin^(2)theta)/((cos theta-sin theta))=(cos theta+sin theta)

Prove each of the following identities : (cos theta) /((1- tan theta)) - (sin^(2) theta)/((cos theta - sin theta)) = (cos theta + sin theta)

Prove that (cos theta)/(1+sin theta)=(1-sin theta)/(cos theta)=sec theta-tan theta

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

Prove that: ((tan theta)/(1-tan theta))-((cot theta)/(1-cot theta))=(cos theta+sin theta)/(cos theta-sin theta)

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

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + cos theta cosec theta