Question 602444
(tan^2 B + 1)/ tanB + cotB  = tanB is NOT an identity but (tan^2 B + 1)/(tanB + cotB)  = tanB is an identity.



Here's why...



(tan^2 B + 1)/(tanB + cotB) = tanB 


(tan^2 B + 1)/(tanB + 1/tanB) = tanB 


(tan^2 B + 1)/(tan^2 B/tanB + 1/tanB) = tanB 


(tan^2 B + 1)/( (tan^2 B + 1)/tanB) = tanB 


(tan^2 B + 1)*(tanB/(tan^2 B + 1)) = tanB 


tanB = tanB 


This verifies the identity.