Chứng minh các đồng nhất thức: `(sinx+sin(x/2))/(1+cosx+cos(x/2))=tan(x/2)`

$\quad \dfrac{\sin x + \sin\left(\dfrac x2\right)}{1 + \cos x + \cos\left(\dfrac x2\right)}$

$= \dfrac{2\sin\left(\dfrac x2\right).\cos\left(\dfrac x2\right) + \sin\left(\dfrac x2\right)}{1 + 2\cos^2\left(\dfrac x2\right) - 1 + \cos\left(\dfrac x2\right)}$

$= \dfrac{\sin\left(\dfrac x2\right)\left[2\cos\left(\dfrac x2\right)+1\right]}{\cos\left(\dfrac x2\right)\left[2\cos\left(\dfrac x2\right)+1\right]}$

$=\dfrac{\sin\left(\dfrac x2\right)}{\cos\left(\dfrac x2\right)}$

$=\tan\left(\dfrac x2\right)$