" 3.Prove ":cosec theta sqrt(1-cos^(2)theta)=1

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

Prove that : ("cosec "theta -cot theta)^(2)=(1-cos theta)/(1+cos 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 that : sqrt((1+cos theta)/(1-costheta))=cosec theta+ cot 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 that : ("cosec "theta-cot theta)^(2)=(1-cos theta)/(1+cos theta) .

Consider the following: 1. sqrt((1-cos theta)/(1+cos theta)) = "cosec" theta -cot theta 2. sqrt((1+cos theta)/(1-cos theta))="cosec" theta +cot theta Which of the above is/are identity/ identities?

Prove that (i) ("cosec"^(2) theta-1 ) tan^(2) theta =1 " " (ii) (sec^(2) theta -1)(1- "cosec"^(2) theta )=-1

Prove that:- sqrt((1+cos theta) / (1-cos theta)) = cosec theta + cot theta

Prove that (1+cosec theta -cot theta)/(1+cosec theta+cot theta)=(1-cos theta)/sin theta.