Prove the identities : `(1+tan^2 theta) (1-sin theta) (1+sin theta) =1`

Prove : ( 1+ tan^2 theta )(1 + sin theta )(1 - sin theta) = 1 .

Prove the following identities: (1-sin theta)/(1+sin theta)=(sec theta-tan theta)^(2)

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

Prove the following identities: (sin theta)/(1-cos theta)+(tan theta)/(1+cos theta)=sec theta cos ect+cot theta

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

Prove the trigonometric identities: (1-sin theta)/(1+sin theta)=(sec theta-tan theta)^(2)

Prove the following trigonometric identities: (tan theta+sin theta)/(tan theta-sin theta)=(sec theta+1)/(sec theta-1)

Prove each of the following identities : (1+ tan^(2) theta)(1+ cot^(2) theta)=(1)/((sin^(2) theta- sin^(4) theta))

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

Prove that (1+sin theta)/(1-sin theta)-(1-sin theta)/(1+sin theta)=4sec theta tan theta