Prove `cosec^2 theta = 1 + cot^2theta`

cosec^(2)theta=1+cot^(2)theta

cosec^2 theta - cot^2 theta = 1 +…..

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

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

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

Prove that cot^4 theta+ cot^2 theta= cosec^4 theta-cosec^2 theta

Prove that : ("cosec "theta -cot theta)^(2)=(1-cos theta)/(1+cos theta)

Prove that : cosec theta + cosec 2 theta + cosec 2^2 theta +...........+cosec2^(n-1) theta= cot(theta/2)-cot 2^(n-1)theta

Prove that: cosec theta +cosec (theta/2)+cosec (theta/2^2)+cosec(theta/2^3)+… to n terms = cot(theta/2^n) -cot theta