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