(-4cos(x)-6sin(x))^2-20sin^2(x)=16

Solución

(- 4 cos (x) - 6 sin (x))^{2} - 20 sin^{2} (x) = 16

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

Pasos de solución

(- 4 cos (x) - 6 sin (x))^{2} - 20 sin^{2} (x) = 16

Restar

16

de ambos lados

16 cos^{2} (x) + 48 cos (x) sin (x) + 16 sin^{2} (x) - 16 = 0

Factorizar

16 cos^{2} (x) + 48 cos (x) sin (x) + 16 sin^{2} (x) - 16 : 16 (cos^{2} (x) + 3 sin (x) cos (x) + sin^{2} (x) - 1)

16 (cos^{2} (x) + 3 sin (x) cos (x) + sin^{2} (x) - 1) = 0

Re-escribir usando identidades trigonométricas

48 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

arccos (x) = arcsin (\frac{1}{4}) + arcsin (\frac{7}{8})

3 cot^{2} (2 t - \frac{3 π}{2}) = 1

3 cot (θ) - 2 = 0

sin (u) = \frac{5}{13}

0.8 = cos (x)