Use

\(\displaystyle{\frac{{{\sec{{\frac{{x}}{{2}}}}}}}{{{\tan{{\frac{{x}}{{2}}}}}+{1}}}}\equiv{\frac{{{1}}}{{{\sin{{\frac{{x}}{{2}}}}}+{\cos{{\frac{{x}}{{2}}}}}}}}\)

Now you have already identified

\(\displaystyle{\left({\sin{{\frac{{x}}{{2}}}}}+{\cos{{\frac{{x}}{{2}}}}}\right)}^{{2}}=?\)

\(\displaystyle{\frac{{{\sec{{\frac{{x}}{{2}}}}}}}{{{\tan{{\frac{{x}}{{2}}}}}+{1}}}}\equiv{\frac{{{1}}}{{{\sin{{\frac{{x}}{{2}}}}}+{\cos{{\frac{{x}}{{2}}}}}}}}\)

Now you have already identified

\(\displaystyle{\left({\sin{{\frac{{x}}{{2}}}}}+{\cos{{\frac{{x}}{{2}}}}}\right)}^{{2}}=?\)