14" Prove the following identities: "(1)/(cosec theta-cot theta)-(1)/(sin theta)=(1)/(sin theta)-(1)/(cosec theta+cot theta)

(1)/(csc theta-cot theta)-(1)/(sin theta)=(1)/(sin theta)-(1)/(csc theta+cot theta)

Prove the following identity : 1/(cosec theta- cot theta)-1/(sin theta) =1/(sin theta)- 1/(cosec theta+cot theta) .

prove that 1/(cosec theta-cot theta) - 1/(sin theta) = 1/sin theta - (1)/(cosec theta + cot theta)

Prove the following identity : (cot^2 theta)/((1- cosec theta)^2)= (1+sin theta)/(1-sin theta) .

Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta)/(1+cos theta)= sec theta cosec theta- cot theta .

Prove the following identity : (tan theta)/(1-cot theta)+ (cot theta)/(1-tan theta)= 1+sec theta cosec theta .

Prove the following identity : (sin theta)/(cot theta+ cosec theta)=2+ (sin theta)/(cot theta- cosec theta) .

Prove that (cos theta-sin theta+1)/(cos theta+sin theta-1)=csc 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

Prove the following identity : (sec theta-cos theta) (cosec theta-sin theta)=1/(tan theta+ cot theta) .