find equations of hte normal plane and osculating place

[maeveoneill]

find equations of hte normal plane and osculating plane of the curve at the given point: r(t)= <cost t, sin t, ln cos t>, (1,0,0).

so far i have
r(t) = cos ti + sin tj + ln cos tk
r'(t) = -sin ti + cost tj -(sin t/cos t)k

|r'(t)|= sqrt of: (-sin t)^2 + (cos t)^2 + (-sin t /cos t) ^2)
= sqrt of sec^2 t
= sec t

then T(t) = r'(t)/ |r' (t)|= -sin ti + cost j - tank tk / sec t
and T'(t) = (sec t)(-cos ti + sin tj - sec^2tk) + (-sin ti + cos tj - tantk)(sect tant) / sec^2
= - cos ti + sin tj - sec^2 tk - (sin t)(tan t)i + sin t - tan^2t / sec t

is this right os far.. and how can i simplify T'(t) further in order to find |T'(t)|?? thanks!