[" 5.(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+ (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) (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

(cot theta)/((cosec theta+1))+((cosec theta+1))/(cot theta)=2sec theta

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

Prove that (tan theta)/(sec theta -1)+ (tan theta)/(sec theta +1) = 2 cosec\ theta

Prove that : (tan theta)/(sec theta -1) + (tan theta)/(sec theta + 1) = 2 cosec theta

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

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

Prove that : (cosec theta)/(cosec theta-1)+ (cosec theta)/ (cosec theta+1)= 2 sec^2 theta .

" (2.) "tan theta+cot theta=sec theta cosec theta