Ayuda con esta demostración de identidad trigonometrica [tex] \ frac{senx}{1 + cosx} + cotx = cscx[ / tex]?

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AL%3D%5Cfrac%7B%5Csin%20x%7D%7B1%2B%5Ccos%20x%7D%2B%5Ccot%20x%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Cfrac%7B%28%5Csin%20x%29%281-%5Ccos%20x%29%7D%7B1-%5Ccos%5E2%20x%7D%2B%5Ccot%20x%5C%5C%20%5C%5C%20%5C%5C%20%0AL%3D%5Cfrac%7B%28%5Csin%20x%29%281-%5Ccos%20x%29%7D%7B%5Csin%5E2%20x%7D%2B%5Ccot%20x%5C%5C%20%5C%5C%20%5C%5C%20%0AL%3D%5Cfrac%7B1-%5Ccos%20x%7D%7B%5Csin%20x%7D%2B%5Ccot%20x%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Ccsc%20x%20-%20%5Ccot%20x%20%2B%5Ccot%20x%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BL%3D%5Ccsc%20x%7D" />.