10.(cosec theta-cot theta)^(2)=?

The value of ("cosec" theta -cot theta)^(2) is

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

If (cosec theta - cot theta)=2 , the (cosec theta +cot theta) is equal to

(1)/(cosec theta+cot theta)=cosec theta-cot theta

(1+cosec theta - cot theta)/(1+cosec theta + cot theta)=

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

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

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