tgx + cosx/(1+sinx)

Thank you for the thumbs up. 

its s*x

Does tgx stand for tangent of x?

And Alexander. Behave yourself!

$$tanx+\frac{cosx}{1+sinx}\\\\
=\frac{sinx}{cosx}+\frac{cosx}{1+sinx}\\\\
=\frac{sinx(1+sinx)}{cosx(1+sinx)}+\frac{(cosx)^2}{(1+sinx)cosx}\\\\
=\frac{sinx+sin^2x+cos^2x}{cosx(1+sinx)}\\\\
=\frac{sinx+1}{cosx(1+sinx)}\\\\
=\frac{1}{cosx}\\\\
=secx$$