SOLUTION: If {{{ (tan^3(x) - 1)/ (tan(x) - 1) - sec^2 (x) + 1 = 0 }}} find cot(x). Unable to solve this trig identity would appreciate help.

Factor the numerator as the difference of cubes: 

Since the denominator tan(x)-1 cannot be 0, tan(x) cannot be 1, so x
cannot be  or 









Now we use the identity  solved for
                        









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Edwin