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

Prove the following identities: (sin theta-cos theta+1)/(sin theta+cos theta-1)=(1+sin theta)/(cos theta)

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

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

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

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

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

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

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

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

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