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

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

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

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

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

(b) cosec theta=1+cot theta

(b) cosec theta=1+cot theta

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

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

(cot theta)/((cosec theta+1))+((cosec theta+1))/(cot theta)=2sec theta

Prove that (1+ cot theta + tan theta ) ( sin theta - cos theta) = (sec theta )/(cosec^(2) theta) - (cosec theta)/(sec^(2)theta) .