prove that `tan A+cot A=2cosec2A`

Prove that tan A - cot A =-2 cot2A

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

Prove that: cotA-cot2A="cosec"2A

If cosec A + sec A = cosec B + sec B , prove that tan A tan B = cot( A+ B)/ 2

Prove that: tan(A/2)+ cot(A/2)=2 "cosec"A

Prove that : (cot^(2) A)/(cosec A - 1) - 1 = cosec A

Prove that : (tan A)/ (1 - cot A) + (cot A)/ (1 - tan A) = sec A cosec A + 1

Prove the identity : tan A + cot A = sec A . cosec A

Prove the following identities : (1)/ (tan A + cot A) = cosec A sin A

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