`1+(cot^(2)theta)/(1+csc theta)=csc theta`

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

Prove each of the following identities : (i) 1+ (cot^(2) theta)/((1+ "cosec"theta))= "cosec" theta (ii) 1+ (tan^(2) theta)/((1+ sec theta))= sec theta

(tan theta)/(sec theta+1)+(cot theta)/(csc theta+1)=csc theta+sec theta-csc theta sec theta

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

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

prove that tan theta/(sec theta+1)+cot theta/(cosec theta+1)=cosec theta+sec theta-cosec theta. sec theta

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

The inverse of [(-cot theta, cosec theta),(cosec theta,-cot theta)] is

If pi lt theta lt 2pi then sqrt ((1+cos theta)/(1-cos theta))= a. cosec theta+cot theta , b. cosec theta - cot theta , c. cot theta-cosec theta , d. -cosectheta - cot theta

(cosec theta)/(cosec theta-1)+(cosec theta)/(cosec theta+1)=2sec^2theta