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

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

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

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

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

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

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 theta-tan theta=2cot 2 theta .

Prove that 1 + tan 2 theta tan theta = sec 2 theta .

Let theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)6(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta), then

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) and t_4=(cot theta)^(cot theta), then