Prove that,
`"cosec" (theta + phi)=("cosec" theta "cosec" phi)/(cot theta + cot phi)`

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 cot 2 theta + tan theta = cosec 2 theta

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

If ("cosec" theta +cot theta)=x find "cosec" theta - cot theta .

Prove that cosec 2alpha = cot alpha - cot 2alpha . Hence or otherwise prove that cosec theta + cosec 2theta + cosec 4theta + cosec 8theta = cot theta/2 - cot 8theta .

Prove that: cot theta + tan theta = cosec theta sec theta .

Prove that: cot theta + tan theta = cosec theta sec theta .

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).

(cot theta + "cosec" theta -1)/( cot theta - "cosec" theta +1) is