Question 602454
(1 - tanX)/(secX) + (secX)/(tanX) = (1+tanX)/(secX tanX) 


(tanX(1 - tanX))/(secX tanX) + (secX)/(tanX) = (1+tanX)/(secX tanX) 


(tanX - tan^2 X))/(secX tanX) + (secX)/(tanX) = (1+tanX)/(secX tanX) 


(tanX - tan^2 X))/(secX tanX) + (secX*secX)/(secX tanX) = (1+tanX)/(secX tanX) 


(tanX - tan^2 X))/(secX tanX) + (sec^2 X)/(secX tanX) = (1+tanX)/(secX tanX) 


(tanX - tan^2 X + sec^2 X)/(secX tanX) = (1+tanX)/(secX tanX) 


(tanX  + sec^2 X - tan^2 X)/(secX tanX) = (1+tanX)/(secX tanX) 


(tanX  + 1)/(secX tanX) = (1+tanX)/(secX tanX)

 
(1 + tanX)/(secX tanX) = (1+tanX)/(secX tanX) 


So we've shown that the original equation is indeed a true identity.