4cos(x)+4sin(x)=2sqrt(6)

Solución

4 cos (x) + 4 sin (x) = 26

x = 0.26179 \dots + 2 πn, x = 1.30899 \dots + 2 πn

Pasos de solución

4 cos (x) + 4 sin (x) = 26

Restar

4 sin (x)

de ambos lados

4 cos (x) = 26 - 4 sin (x)

Elevar al cuadrado ambos lados

(4 cos (x))^{2} = (26 - 4 sin (x))^{2}

Restar

(26 - 4 sin (x))^{2}

de ambos lados

16 cos^{2} (x) - 24 + 166 sin (x) - 16 sin^{2} (x) = 0

Re-escribir usando identidades trigonométricas

- 8 - 32 sin^{2} (x) + 16 sin (x) 6 = 0

Usando el método de sustitución

sin (x) = \frac{6 - 2}{4}, sin (x) = \frac{6 + 2}{4}

sin (x) = \frac{6 - 2}{4} : x = arcsin (\frac{6 - 2}{4}) + 2 πn, x = π - arcsin (\frac{6 - 2}{4}) + 2 πn

sin (x) = \frac{6 + 2}{4} : x = arcsin (\frac{6 + 2}{4}) + 2 πn, x = π - arcsin (\frac{6 + 2}{4}) + 2 πn

Combinar toda las soluciones

x = arcsin (\frac{6 - 2}{4}) + 2 πn, x = π - arcsin (\frac{6 - 2}{4}) + 2 πn, x = arcsin (\frac{6 + 2}{4}) + 2 πn, x = π - arcsin (\frac{6 + 2}{4}) + 2 πn

Verificar las soluciones sustituyendo en la ecuación original

x = arcsin (\frac{6 - 2}{4}) + 2 πn, x = arcsin (\frac{6 + 2}{4}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.26179 \dots + 2 πn, x = 1.30899 \dots + 2 πn

7 tan^{2} (θ) - 4 tan (θ) = 0, - 9 0^{\circ} \leq θ \leq 9 0^{\circ}

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

2 tan^{2} (α) = 2 tan (α)

cos^{2} (x) - sin^{2} (x) = - \frac{3}{4}

8 cos (8 x) = 0