" 8.(i) "1+(cot^(2)theta)/((1+cosec theta))=cosec 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

1+(cot^(2)theta)/(1+csc theta)=csc theta

show that 1 + (cot^2 theta/ (1 + cosec theta)) = cosec theta

(b) cosec theta=1+cot theta

(b) cosec theta=1+cot theta

Prove that (cot^(2)theta)/(cosec theta+1)=cosec theta-1

Prove that: (sin theta)/(1 - cos theta) + (tan theta)/(1 + cos theta) = cosec theta + cot theta + sec theta cosec theta - cosec theta

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