Question 230798
(cotX * cosX)/(cotX + cosX) = (cotX - cosX)/(cotX * cosX) 
---------
Since it's all x I'll leave it out.
Cross multiply
(cot*cos)^2 = cot^2 - cos^2
(cos^2/sin^2)*cos^2 = (cos^2/sin^2) - cos^2
Divide out cos^2
cos^2/sin^2 = (1/sin^2) - 1 
cos^2/sin^2 = (1 - sin^2)/sin^2 
cos^2/sin^2 = cos^2/sin^2
---------------------------
PS  If you sub a value and it doesn't work, you know it's not an identity.  
If a value does work, that doesn't guarantee it works for all values.