[" Prove each of the following identiti "],[" 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

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) cot^(2) theta - (1)/(sin^(2) theta)=-1 " " (ii) tan^(2) theta - (1)/(cos^(2) theta)=-1 (iii) cos^(2) theta + (1)/((1+ cot^(2) theta))=1

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) sin^(2)theta + cos^(4) theta = cos^(2) theta + sin^(4) theta (ii) "cosec"^(4) theta - "cosec"^(2) theta = cot^(4) theta + cot^(2) theta

Prove each of the following identities : (i) sin^(6) theta + cos^(6)theta = 1- 3 sin^(2) theta cos^(2) theta (ii) sin^(2)theta + cos^(4) theta = cos^(2) theta + sin^(4) theta (iii) "cosec"^(4) theta - "cosec"^(2) theta = cot^(4) theta + cot^(2) 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 : (i) sec theta(1- sin theta)(sec theta + tan theta)=1 (ii) sin theta (1+ tan theta) + cos theta( 1+ cot theta)=( sec theta + "cosec" theta)

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

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