[" Prove the following identities: "],[qquad (1+cos theta)(1-cos theta)(1+cot^(2)theta)=1]

Prove each of the following identities : (i) (1+ cos theta)(1- cos theta)(1+ cot^(2) theta)=1 (ii) "cosec" theta (1+ cos theta)("cosec" theta - cot theta)=1

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

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

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

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

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

Prove the following identity : sqrt ((1+cos theta)/ (1-cos theta)) = cosec theta+cot theta

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

Prove the following identity : (1+cos theta)/(1-cos theta)= (tan^2 theta)/((sec theta-1)^2) .

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