bentuk sederhana dari sin x + tan x / 1 + cos x

[tex]$\begin{align}\frac{\sin x+\tan x}{1+\cos x}&=\frac{\sin x+\dfrac{\sin x}{\cos x}}{1+\cos x}\\&=\frac{~\dfrac{\sin x\cos x+\sin x}{\cos x}~}{1+\cos x}\\&=\frac{\sin x\cos x+\sin x}{\cos x(1+\cos x)}\\&=\frac{\sin x(\cos x+1)}{\cos x(\cos x+1)}\\&=\frac{\sin x}{\cos x}\\&=\boxed{\tan x}\end[/tex]