Question 573724
Cross-multiply


*[tex \LARGE (1+\sec x)(\cos x - 1) = (1-\sec x)(\cos x+1)]


*[tex \LARGE \cos x - 1 + \sec x \cos x - \sec x = \cos x + 1 - \sec x \cos x - \sec x]


Note that sec x cos x = 1. Replacing this, we have


*[tex \LARGE \cos x - 1 + 1 - \sec x = \cos x + 1 - 1 - \sec x]


*[tex \LARGE \cos x - \sec x = \cos x - \sec x]


This is true for all x (such that sec x is defined) so the original equation is also true.