90-70sin(x)-130cos(x)=0

Solución

90 - 70 sin (x) - 130 cos (x) = 0

x = 1.40923 \dots + 2 πn, x = - 0.42135 \dots + 2 πn

Pasos de solución

90 - 70 sin (x) - 130 cos (x) = 0

Sumar

130 cos (x)

a ambos lados

90 - 70 sin (x) = 130 cos (x)

Elevar al cuadrado ambos lados

(90 - 70 sin (x))^{2} = (130 cos (x))^{2}

Restar

(130 cos (x))^{2}

de ambos lados

(90 - 70 sin (x))^{2} - 16900 cos^{2} (x) = 0

Re-escribir usando identidades trigonométricas

- 8800 - 12600 sin (x) + 21800 sin^{2} (x) = 0

Usando el método de sustitución

sin (x) = \frac{63 + 13 137}{218}, sin (x) = \frac{63 - 13 137}{218}

sin (x) = \frac{63 + 13 137}{218} : x = arcsin (\frac{63 + 13 137}{218}) + 2 πn, x = π - arcsin (\frac{63 + 13 137}{218}) + 2 πn

sin (x) = \frac{63 - 13 137}{218} : x = arcsin (\frac{63 - 13 137}{218}) + 2 πn, x = π + arcsin (- \frac{63 - 13 137}{218}) + 2 πn

Combinar toda las soluciones

x = arcsin (\frac{63 + 13 137}{218}) + 2 πn, x = π - arcsin (\frac{63 + 13 137}{218}) + 2 πn, x = arcsin (\frac{63 - 13 137}{218}) + 2 πn, x = π + arcsin (- \frac{63 - 13 137}{218}) + 2 πn

Verificar las soluciones sustituyendo en la ecuación original

x = arcsin (\frac{63 + 13 137}{218}) + 2 πn, x = arcsin (\frac{63 - 13 137}{218}) + 2 πn

Mostrar soluciones en forma decimal

x = 1.40923 \dots + 2 πn, x = - 0.42135 \dots + 2 πn

2 sin (x) sec (x) - 23 sin (x) = 0

cot (a) sec (a) = cos (a)

cos (2 x) 2 cos (x) = 2 (2 cos^{2} (x) - 1) 2 cos (x)

4 sin^{2} (x) = 4 cos (x) + 1

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