+1768 Let x be an acute angle such that \tan x + \sec x = \cos x. Find \cos x.
+129883 \( \tan x + \sec x = \cos x \)
sin x / cos x + 1 /cos x = cos x
sin x + 1 = cos^2 x
sin x + 1 = 1 - sin^2 x
sin^2 x + sin x = 0
sin x ( sin x + 1) = 0
sin x = 0 x = 0 so cos 0 = 1
sin x = -1 x = pi /2 so cos pi /2 = 0 {reject because sec pi /2 is undefined }
So
cos x = cos 0 = 1
