Simplify the expression:

1 + sinx/cosx + cosx/1 + sinx

1 + cosX / (1+sinX) + (1+sinX) / cosX

add the two fractions using common denominator as: cosx (1+sinx)

we get:

=1 + cos^2x + (1+sinx) ^2/cosx (1+sinx)

=1 + cos^2x+1+2sinx+sin^2x/cosx (1+sinx)

cos^2x+sin^2x=1

=1 + 2+2sinx/cosx (1+sinx)

=1 + 2 (1+sinx) / cosx (1+sinx)

= 1 + 2/cosx

=1 + 2secx