Write each expression in terms of sines and/or cosines and then simplify.

(cos (x) tan (x) + 1) (sin (x) - 1) / cos^2 (x)

Tan (x) = sin (x) / cos (x), therefore, substitute sin (x) / cos (x) in the expression:

= (cos (x) (sin (x) / cos (x)) - 1) / cos^2 (x)

simplify the 2 cos (x):

= (sin (x) - 1) / cos^2 (x)

Sin^2 (x) + cos^2 (x) = 1, sin^2 (x) - 1 = - cos^2 (x), substitute in the expression:

= - cos^2 (x) / cos^2 (x) = - 1