(-5cos(x)-6sin(x))^2-11sin^2(x)=25

Solución

(- 5 cos (x) - 6 sin (x))^{2} - 11 sin^{2} (x) = 25

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn

Pasos de solución

(- 5 cos (x) - 6 sin (x))^{2} - 11 sin^{2} (x) = 25

Restar

25

de ambos lados

25 cos^{2} (x) + 60 cos (x) sin (x) + 25 sin^{2} (x) - 25 = 0

Re-escribir usando identidades trigonométricas

60 cos (x) sin (x) = 0

Resolver cada parte por separado

cos (x) = 0 or sin (x) = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combinar toda las soluciones

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn

sec^{2} (x) + \frac{1}{2} \cdot sec (x) = 0

2 sin^{2} (x) - 9 sin (x) - 5 = 0

2 sin (a) - 3 = 0

sin (x) = - \frac{3}{2}

- \frac{π}{2} = π cos (θ)