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

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

Prove that : (cosec theta)/(cosec theta-1)+ (cosec theta)/ (cosec theta+1)= 2 sec^2 theta .

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

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

Prove that cot 2 theta + tan theta = cosec 2 theta

(1+cosec theta - cot theta)/(1+cosec theta + cot 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 cot^4 theta+ cot^2 theta= cosec^4 theta-cosec^2 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 .

show that 1 + (cot^2 theta/ (1 + cosec theta)) = cosec theta