`cos theta . Cosec theta = cot 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

Find cos theta, if 6 cot theta+2 "cosec" theta= cot theta+5 "cosec" theta .

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

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

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

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

Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta)/(1+cos theta)= sec theta cosec theta- cot theta .

Prove that : sqrt((1+cos theta)/(1-costheta))=cosec theta+ cot theta .

( sec theta + tan theta )/("cosec " theta + cot theta ) -(sec theta - tan theta )/( " cosec" theta - cot theta )=