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) = (sec theta cosec theta +1)

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

Prove that : (sin theta + sec theta) ^(2) + (cos theta + cosec theta) ^(2) = (1 + sec theta cosec theta) ^(2).

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

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

Solve cot theta + tan theta=2 cosec theta .

Prove that : (tan^(2)theta)/(1+tan^(2)theta)+(cot^(2)theta)/(1+cot^(2)theta)=1

Let theta in ( 0, pi/4) and t_1 = (tan theta)^(tan theta) , t_2 = (tan theta)^(cot theta), t_3 = ( cot theta)^(tan theta), t_4=(cot theta)^(cot theta) , then

Prove that cot 2 theta + tan theta = cosec 2 theta

Prove that ("sin"theta)/(1-"cot"theta)+("cos"theta)/(1-"tan"theta)="cos"theta+"sin"theta