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

Prove that (1+sin theta)/(csc theta-cot theta)-(1-sin theta)/(csc theta+cot theta)=2(1+cot 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 sin theta(1+tan theta)+cos theta(1+cot theta)=sec theta+cos ec theta

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

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

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

Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta)/(1+cos theta)= sec theta cosec theta- cot theta .

prove that tan theta/(sec theta+1)+cot theta/(cosec theta+1)=cosec theta+sec theta-cosec theta. sec theta

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