सिद्ध कीजिए `(cos theta-sin theta+1)/(cos theta+sin theta-1)=cosec theta+cot theta`

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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

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

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

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

(cos^(2)theta)/(sin theta)-cosec theta+sin theta=0

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

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

(cosec theta -sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) = 1.