" 21."(i)(cos^(2)theta(1-cos theta))/(sin^(2)theta(1-sin theta))=(1+sin theta)/(1+cos theta)

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

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

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

(sin^(2) theta)/(1-cos theta)-(cos^(2) theta)/(1-sin theta)=cos theta-sin theta

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

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

1-(sin^(2)theta)/(1+cos theta)+(1+cos theta)/(sin theta)-(sin theta)/(1-cos theta) equals

(1 + sin theta-cos theta) / (1 + sin theta + cos theta)

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

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)