Me ayudan en este ejercicio es urgente pliss 4sen ^ 4 x - 7sen ^ 2 x + 3 = 0?

4sen ^ 4(X) - 7sen ^ 2(X) + 3 = 0

Hacemos un cambio de Variable

U = sen(X)

4U ^ 4 - 7U² + 3 = 0

Nuevamente otro cambio de Variable

V = U²

4V² - 7V + 3 = 0 ; a = 4 ; b = - 7 ; c = 3

<img src="https://tex.z-dn.net/?f=V%3D%5Cfrac%7B-%28-7%29%5Cpm%20%5Csqrt%7B%28-7%29%5E2-4%284%29%283%29%7D%7D%7B2%284%29%7D" />

<img src="https://tex.z-dn.net/?f=V%3D%5Cfrac%7B7%5Cpm%20%5Csqrt%7B%2849-48%29%7D%7D%7B8%7D" />

V = [7 + / - 1] / 8

V1 = (7 + 1) / 8 = 1

V2 = (7 - 1) / 8 = 0.

75

Ahora como V = U²

<img src="https://tex.z-dn.net/?f=U1%3D%2B%2F-%20%5Csqrt%7B1%7D%20" />

<img src="https://tex.z-dn.net/?f=U2%3D%2B%2F-%20%5Csqrt%7B0.75%7D%20" />

U1 = + 1, - 1

U2 = + 0.

866025, - 0.

866025

Como U = sen(X)

<img src="https://tex.z-dn.net/?f=1%3Dsen%28X%29%3BX%3Dsen%5E%7B-1%7D%281%29%3D90%20" />

<img src="https://tex.z-dn.net/?f=-1%3Dsen%28X%29%3BX%3Dsen%5E%7B-1%7D%28-1%29%3D-90" />

X1 = 90° , - 90°

U2 = 0.

866025 , - 0.

866025

<img src="https://tex.z-dn.net/?f=0.866025%3Dsen%28X%29%3BX%3Dsen%5E%7B-1%7D%280.866025%29%3D60" />

<img src="https://tex.z-dn.net/?f=-0.866025%3Dsen%28X%29%3BX%3Dsen%5E%7B-1%7D%28-0.866025%29%3D-60" />

X2 = 60° , - 60°

Finalmente las Soluciones son :

X = - 90° , - 60°, 60°, 90°.