[" 47.(i) "(1+cos theta+sin theta)/(1+cos theta-sin theta),=(1+sin theta)/(cos theta)],[cos theta-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)

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)

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

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

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

(sin theta)/(1+cos theta)+(1+cos theta)/(sin theta)=2cos ec theta

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