El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\cos{\left(x \right)} + \frac{\cos{\left(2 x \right)}}{2} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = i \left(\log{\left(2 \right)} - \log{\left(-1 + \sqrt{3} - \sqrt{2} \sqrt[4]{3} i \right)}\right)$$
$$x_{2} = i \left(\log{\left(2 \right)} - \log{\left(-1 + \sqrt{3} + \sqrt{2} \sqrt[4]{3} i \right)}\right)$$
Solución numérica$$x_{1} = -1.19606189408616$$
$$x_{2} = -114.293397423319$$
$$x_{3} = 61.6357911777097$$
$$x_{4} = 51.4615443515228$$
$$x_{5} = 11.370308720273$$
$$x_{6} = -45.1783590443433$$
$$x_{7} = -67.9189764848893$$
$$x_{8} = 80.4853470992485$$
$$x_{9} = 64.027914965882$$
$$x_{10} = -30.2198646418118$$
$$x_{11} = -23.9366793346322$$
$$x_{12} = 32.6119884299841$$
$$x_{13} = 82.8774708874208$$
$$x_{14} = -93.0517177136076$$
$$x_{15} = 13.7624325084453$$
$$x_{16} = 95.44384150178$$
$$x_{17} = 101.72702680896$$
$$x_{18} = 86.7685324064281$$
$$x_{19} = -55.3526058705301$$
$$x_{20} = 38.8951737371637$$
$$x_{21} = -57.7447296587024$$
$$x_{22} = -99.3349030207872$$
$$x_{23} = 1695.2639710444$$
$$x_{24} = -36.5030499489914$$
$$x_{25} = 20.0456178156249$$
$$x_{26} = -74.2021617920689$$
$$x_{27} = 55.3526058705301$$
$$x_{28} = -70.3111002730616$$
$$x_{29} = -61.6357911777097$$
$$x_{30} = 57.7447296587024$$
$$x_{31} = 26.3288031228045$$
$$x_{32} = 76.5942855802412$$
$$x_{33} = 67.9189764848893$$
$$x_{34} = -20.0456178156249$$
$$x_{35} = 7.47924720126574$$
$$x_{36} = -17.6534940274526$$
$$x_{37} = -5.08712341309343$$
$$x_{38} = -64.027914965882$$
$$x_{39} = -51.4615443515228$$
$$x_{40} = -89.1606561946004$$
$$x_{41} = 42.7862352561709$$
$$x_{42} = -49.0694205633505$$
$$x_{43} = -13.7624325084453$$
$$x_{44} = 99.3349030207872$$
$$x_{45} = -76.5942855802412$$
$$x_{46} = -95.44384150178$$
$$x_{47} = -26.3288031228045$$
$$x_{48} = 114.293397423319$$
$$x_{49} = -667.213704455122$$
$$x_{50} = 17.6534940274526$$
$$x_{51} = -80.4853470992485$$
$$x_{52} = -7.47924720126574$$
$$x_{53} = 70.3111002730616$$
$$x_{54} = 30.2198646418118$$
$$x_{55} = 74.2021617920689$$
$$x_{56} = 36.5030499489914$$
$$x_{57} = 23.9366793346322$$
$$x_{58} = 2344.82418147207$$
$$x_{59} = -11.370308720273$$
$$x_{60} = 93.0517177136076$$
$$x_{61} = -101.72702680896$$
$$x_{62} = -32.6119884299841$$