4cos^2(x)+3sin^2(x)-4=-tan^2(x)

Solución

4 cos^{2} (x) + 3 sin^{2} (x) - 4 = - tan^{2} (x)

x = 2 πn, x = π + 2 πn

Pasos de solución

4 cos^{2} (x) + 3 sin^{2} (x) - 4 = - tan^{2} (x)

Restar

- tan^{2} (x)

de ambos lados

4 cos^{2} (x) + 3 sin^{2} (x) - 4 + tan^{2} (x) = 0

Re-escribir usando identidades trigonométricas

- sin^{2} (x) + tan^{2} (x) = 0

Factorizar

- sin^{2} (x) + tan^{2} (x) : (tan (x) + sin (x)) (tan (x) - sin (x))

(tan (x) + sin (x)) (tan (x) - sin (x)) = 0

Resolver cada parte por separado

tan (x) + sin (x) = 0 or tan (x) - sin (x) = 0

tan (x) + sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) - sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn

tan^{2} (x) - 2 = 3 tan (x)

3 cos (x) + sin (x) = 3

2 tan^{2} (θ) - 2 = 0

sin^{2} (x) = 2 - sin (x)

2 csc (x) cos (x) = csc (x)