trigo derivatives help

[serenaleesl]

lim(x->0) (sin(cos x) / sec x)
my steps :
cos x sin(cos x) / sec x cos x
= (cosx)^2
= 1.
but the answer is sin 1...what's up with this?

 

[skeeter]

lim(x->0) (sin(cos x) / sec x)
my steps :
cos x sin(cos x) / sec x cos x
= cos x sin(cos x)/1

lim{x-> 0} cos x sin(cos x) = cos 0 sin(cos 0) = 1 * sin(1) = sin(1)