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

(1+tan^2theta) sin^2theta

Prove the identities: (1+cot theta - cosec theta) (1+ tan theta + sec theta)=2

Solve the equation (1-tan theta) (1+ sin 2theta) = 1 + tan theta

Prove the following identities: (cos^2theta)/(1-tantheta)+(sin^3theta)/(sintheta-costheta)=1+sinthetacostheta

Prove the identity ((1-tan theta)/(1-cot theta))^(2)=tan^(2)theta

Prove the following identities : sqrt((1+sin theta)/(1-sin theta)) = sec theta + tan theta where theta is a acute

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

Prove that : (1+ sin theta)/(1-sin theta) = tan^2 (pi/4 + theta/2)

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

Prove the following trigonometric identities : cot^2theta-1/(sin^2theta)=-1 (ii) (1+tan^2theta)(1+sintheta)(1-sintheta)=1