`(tan theta)/(sec theta -1)+ (tan theta)/(sec theta +1) = 2 cosec\ theta`

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

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

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

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

(tan theta)/(sec theta+1)+(sec theta+1)/(tan theta)=2cos ec theta

1+(tan^(2)theta)/((1+sec theta))=sec theta

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