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

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

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

Prove :(cos theta)/(1+sin theta)+(cos theta)/(1-sin theta)=2sec theta

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

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

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

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

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

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

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