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

( sec theta + tan theta )/("cosec " theta + cot theta ) -(sec theta - tan theta )/( " cosec" theta - cot theta )=

Prove each of the following identities : (i) ("cosec"theta + cot theta )/("cosec"theta - cot theta ) = ("cosec" theta + cot theta)^(2) = 1+2cot^(2) theta + 2"cosec" theta cot theta (ii) (sec theta + tan theta ) /( sec theta - tan theta) =(sec theta + tan theta )^(2) = 1+ 2tan^(2) theta + 2 sec theta tan theta

x=sec theta-tan theta, y=cosec theta+cot theta, then

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

(sec theta+tan theta)/(csc theta+cot theta)=(csc theta-cot theta)/(sec theta-tan theta)

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

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

Prove that (1+cot theta -"cosec" theta ) (1+ tan theta + sec theta )=2 .