Imagen ayuda, para resolver?

<img src="https://tex.z-dn.net/?f=h%28x%29%3D%5Ccos%20x%5C%5C%5B4pt%5DM%3D%5Cdfrac%7Bh%28x%2Bk%29-h%28x%29%7D%7Bk%7D%3D%5Cdfrac%7B%5Ccos%20%28x%2Bk%29-%5Ccos%20x%7D%7Bk%7D%20%20%5C%20%20%5C%20%2C%20%5C%20%5C%20k%5C%20%5Ctextgreater%20%5C%200%5C%5C%5B4pt%5D%0A%5Ctext%7BAll%5C%27i%20puede%20quedar%20o%20se%20pude%20desarrollar%20ese%20coseno%20de%20la%20suma%7D%20%5C%5C%5B4pt%5D%0AM%3D%5Cdfrac%7B%5Ccos%20x%20%5C%2C%5Ccos%20k-%5Csin%20x%20%5C%2C%5Csin%20k-%5Ccos%20x%7D%7Bk%7D%20%0A" />

<img src="https://tex.z-dn.net/?f=%5Ctext%7BSe%20podr%5C%27ia%20factorizar%20o%20incluso%20desde%20el%20inicio%20convertir%20de%20una%20%7D%5C%5C%0A%5Ctext%7Bdiferencia%20a%20producto%20%2C%20pero%20la%20pregunta%20es%20con%20que%20prop%5C%27osito%20%3F%7D%20%5C%5C%5B4pt%5D%0A%5Ctext%7BSi%20el%20fin%20es%20simplificar%20el%20factor%20%7Dk%20%5Ctext%7B%20del%20denominador%20%2C%20pues%20en%20este%7D%5C%5C%0A%5Ctext%7Bejercicio%20no%20hay%20manera%20de%20hacer%20eso.%7D" />

<img src="https://tex.z-dn.net/?f=%5Ctext%7BEn%20la%20imagen%20adjunta%20dejo%20como%20ser%5C%27ia%20en%20caso%20sea%20un%20l%5C%27imite%20%2C%20all%5C%27i%20%7D%5C%5C%0A%5Ctext%7Bel%20ejercicio%20%20s%5C%27i%20%20tiene%20sentido.%7D" />.