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

cos theta+sin theta=cos2 theta+sin2 theta

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

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

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

Prove: (cos^(3)theta+sin^(3)theta)/(cos theta+sin theta)+(cos^(3)theta-sin^(3)theta)/(cos theta-sin theta)=2

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta

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

(sin theta)/(cos3 theta)+(sin3 theta)/(cos9 theta)+(sin9 theta)/(cos27 theta)+(sin27 theta)/(cos81 theta)=