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

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

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

Prove that sin theta(1+tan theta)+cos theta(1+cot theta)=sec theta+cos ec theta

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

( 1 + tan theta + sec theta ) ( 1 + cot theta - cosec theta ) =

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

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

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

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

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