Me ayudan en este ejercicio x favor cos2x + cosx = 0 urgentw?

Cos(2X) + cos(X) = 0

cos(2X) = 2cos²(X) - 1

2cos²(X) - 1 + cos(X) = 0

2cos²(X) + cos(X) - 1 = 0

Hacemos un cambio de variable ; U = cos(X)

2U² + U - 1 = 0 ; Donde a = 2 ; b = 1, c = - 1

<img src="https://tex.z-dn.net/?f=U%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D" />

<img src="https://tex.z-dn.net/?f=U%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2-4%282%29%28-1%29%7D%7D%7B2%282%29%7D" />

<img src="https://tex.z-dn.net/?f=U%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%2B8%7D%7D%7B4%7D" />

<img src="https://tex.z-dn.net/?f=U%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B9%7D%7D%7B4%7D" />

U = [ - 1 + / - 3] / 4

U1 = ( - 1 + 3) / 4 = 1 / 2

U2 = ( - 1 - 3) / 4 = - 1

Como U = cos(X)

1 / 2 = cos(X) ;

<img src="https://tex.z-dn.net/?f=X%3Dcos%20%5E%7B-1%7D%281%2F2%29%3D60%20" />

X1 = 60° - 1 = cos(X)

<img src="https://tex.z-dn.net/?f=X2%3Dcos%5E%7B-1%7D%28-1%29%3D180%20" />

X2 = 180°

X = 60° , 180°.