this question was given on a practice test

y = sec(x)csc(x)tan(x) Determine if there are any vertical asymptotes or holes

The answer given was

Y = sin(x)/[cos(x)sin(x)] = 1/cos(x)

Therefore, there are holes at x =0, pi, 2pi, etc, and vertical asymptotes at x = pi/2, 3pi/2, etc

Should't the answer be y= 1 / cos^2(x) ?

And can someone please explain to me how you find holes in this type of function?

Thanks!