Evaluate: lim_x→π/2 [(1 - sin x) / cos x]

lim_x→π/2 [(1 - sin x) / cos x] 

= lim_y→0 [(1 - sin(π/2 - y)) / cos(π/2 - y)]   (taking π/2 - x = y)

= lim_y→0 [(1 - cosy) / siny]

= lim_y→0 [(2sin²(y/2)) / (2sin(y/2) cos(y/2))]

= lim_y→0 tan(y/2)

= 0