[" Prove ach of the following identitios: "],[" 1.(i) "(1-cos^(2)theta)csc^(2)theta=1]

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

(1-cos^2 theta) cosec^2 theta=1

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

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

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 each of the following identities : (sin theta)/((1+ cos theta)) + ((1+ cos theta))/(sin theta) = 2 "cosec" theta

Prove each of the following identities : (i) sqrt((1+ sin theta)/(1- sin theta)) = ( sec theta + tan theta) (ii) sqrt((1- cos theta)/(1+ cos theta))= ("cosec" theta - cot theta) (iii) sqrt((1+ cos theta)/(1- cos theta))+ sqrt((1- cos theta)/(1+ cos theta)) = 2 "cosec" theta

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

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

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