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

Prove that (sin theta )/( 1 + cos theta) + (1 + cos theta )/( sin theta) = 2 cosec 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 (i) (1- sin theta)/(1+ sin theta)=(sec theta - tan theta )^(2) (ii) ((1+cos theta))/((1- cos theta))= ("cosec" theta + cot theta)^(2)

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

((sec theta + tan theta) (1- sin theta))/(cosec theta (1 + cos theta)(cosec theta - cot theta)) is equal to: ((sec theta + tan theta) (1- sin theta))/(cosec theta (1 + cos theta)(cosec theta - cot theta)) बराबर है :

If "cosec"^(2) theta (1 + cos theta ) (1 - cos theta) = alpha then find the value of alpha .