how do you prove

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

\frac{cos(x)}{1+sin(x)}+\frac{1+sin(x)}{cos(x)}

=\frac{cos^{2}(x)+1+2sin(x)+sin^{2}(x)}{cos(x)(1+s in(x))}

=\frac{2+2sin(x)}{cos(x)(1+sin(x))}

Now, factor the numerator, cancel and see what remains.