how do you simplify "[sin(x)+tan(x)]/[1+sec(X)]"

Answer 1

Changing everything to sines and cosines usually works
[sin(x)+tan(x)]/[1+sec(X)]
= (sinx + sinx/cosx)/(1 + 1/cosx)
= [(sinxcosx + sinx)/cosx]/[(cosx + 1)/cosx]
= [sinx(cosx + 1)/cosx][cosx/(cosx + 1)]
= sinx