ubrace((iii))(cos theta-sin theta+1)/(cos theta+sin theta-1)=cosec theta+cot theta

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

(cosec theta+sin theta)(cosec theta-sin theta)=cot^(2)theta+cos^(2)theta

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

(cos theta cosec theta-sin theta sec theta)/(cos theta+sin theta)=cosec theta-sec theta

(cosec theta-sin theta)(sec theta-cos theta)=sin theta. cos theta

csc theta(1+cos theta)(csc theta-cot theta)=1

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

(sin theta)/(cosec theta)+(cos theta)/(sec theta)=1

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

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