" 5.(i) "1+(cot^(2)theta)/((1+csc theta))=csc 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

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

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

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

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

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

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

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