$\frac{cosx}{1+sinx}+\frac{1+sinx}{cosx}$ is equal to :

2sin x 2cos x 2cosec x 2sec x

2sec x

\(\frac{cosx }{1+sinx}\) + \(\frac{1+sinx }{cosx}\) = \(\frac{cos²x + (1 + sinx )² }{cosx(1+sinx)}\) = \(\frac{cos²x +sin²x  + 1 + 2sinx}{cosx(1+sinx)}\) = \(\frac{2+ 2sinx}{cosx(1+sinx)}\) = 2secx