`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 that : (sin theta)/(1 - costheta) = cosec theta + cot 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 that (1+sin theta)/(csc theta-cot theta)-(1-sin theta)/(csc theta+cot theta)=2(1+cot theta)

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

cosec^(2)theta-cot^(2)theta-1

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