Prove that :
`(tan theta)/(sec theta -1) + (tan theta)/(sec theta + 1) = 2 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 that (tan theta) / (sec theta -1) = (tan theta + sec theta + 1) / (tan theta + sec theta - 1)

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

Prove that (sec 8theta-1)/(sec 4 theta -1) = (tan 8theta)/(tan 2theta)

Prove that (sec 8theta-1)/(sec 4 theta -1) = (tan 8theta)/(tan 2theta)

Prove that : (sec 8theta - 1)/(sec 4theta - 1) = (tan 8theta)/(tan 2theta)

Prove that (sec4 theta-1)/(sec2 theta-1)=(tan4 theta)/(tan theta)

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