How do you solve cos(x)/Tan(x) + Sec(x)

cosx/(tanx +secx)=
cosx/[sinx/cosx+1/cosx]=
cos^2(x)/(1+sinx)=
1-sin^2(x)/(1+sinx)=
(1-sinx)(1+sinx)/(1+sinx)=
1 - sinx

Do you want to simplify it?
cos x /(tan x + sec x)
= cos x (-tan x + sec x)/(-tan^2 x + sec^2 x)
= 1 - sin x