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Popular >

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

Solución

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

Solución

x = 1.22069 \dots + 2 πn, x = π - 1.22069 \dots + 2 πn, x = - 1.22069 \dots + 2 πn, x = π + 1.22069 \dots + 2 πn

Grados

x = 69.94041 \dots^{\circ} + 36 0^{\circ} n, x = 110.05958 \dots^{\circ} + 36 0^{\circ} n, x = - 69.94041 \dots^{\circ} + 36 0^{\circ} n, x = 249.94041 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Restar

(4 cos (x))^{2}

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad pitagórica:

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

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

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

Simplificar

1 + sin^{2} (x) - 16 (1 - sin^{2} (x)) : 17 sin^{2} (x) - 15

1 + sin^{2} (x) - 16 (1 - sin^{2} (x))

Expandir

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

- 16 (1 - sin^{2} (x))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = - 16, b = 1, c = sin^{2} (x)

= - 16 \cdot 1 - (- 16) sin^{2} (x)

Aplicar las reglas de los signos

- (- a) = a

= - 16 \cdot 1 + 16 sin^{2} (x)

Multiplicar los numeros:

16 \cdot 1 = 16

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

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

Simplificar

1 + sin^{2} (x) - 16 + 16 sin^{2} (x) : 17 sin^{2} (x) - 15

1 + sin^{2} (x) - 16 + 16 sin^{2} (x)

Agrupar términos semejantes

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

Sumar elementos similares:

sin^{2} (x) + 16 sin^{2} (x) = 17 sin^{2} (x)

= 17 sin^{2} (x) + 1 - 16

Sumar/restar lo siguiente:

1 - 16 = - 15

= 17 sin^{2} (x) - 15

= 17 sin^{2} (x) - 15

= 17 sin^{2} (x) - 15

- 15 + 17 sin^{2} (x) = 0

Usando el método de sustitución

- 15 + 17 sin^{2} (x) = 0

Sea:

sin (x) = u

- 15 + 17 u^{2} = 0

- 15 + 17 u^{2} = 0 : u = \frac{15}{17}, u = - \frac{15}{17}

- 15 + 17 u^{2} = 0

Mover

15

al lado derecho

- 15 + 17 u^{2} = 0

Sumar

15

a ambos lados

- 15 + 17 u^{2} + 15 = 0 + 15

Simplificar

17 u^{2} = 15

17 u^{2} = 15

Dividir ambos lados entre

17

17 u^{2} = 15

Dividir ambos lados entre

17

\frac{17 u ^{2}}{17} = \frac{15}{17}

Simplificar

u^{2} = \frac{15}{17}

u^{2} = \frac{15}{17}

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = \frac{15}{17}, u = - \frac{15}{17}

Sustituir en la ecuación

u = sin (x)

sin (x) = \frac{15}{17}, sin (x) = - \frac{15}{17}

sin (x) = \frac{15}{17}, sin (x) = - \frac{15}{17}

sin (x) = \frac{15}{17} : x = arcsin (\frac{15}{17}) + 2 πn, x = π - arcsin (\frac{15}{17}) + 2 πn

sin (x) = \frac{15}{17}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{15}{17}

Soluciones generales para

sin (x) = \frac{15}{17}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{15}{17}) + 2 πn, x = π - arcsin (\frac{15}{17}) + 2 πn

x = arcsin (\frac{15}{17}) + 2 πn, x = π - arcsin (\frac{15}{17}) + 2 πn

sin (x) = - \frac{15}{17} : x = arcsin (- \frac{15}{17}) + 2 πn, x = π + arcsin (\frac{15}{17}) + 2 πn

sin (x) = - \frac{15}{17}

Aplicar propiedades trigonométricas inversas

sin (x) = - \frac{15}{17}

Soluciones generales para

sin (x) = - \frac{15}{17}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{15}{17}) + 2 πn, x = π + arcsin (\frac{15}{17}) + 2 πn

x = arcsin (- \frac{15}{17}) + 2 πn, x = π + arcsin (\frac{15}{17}) + 2 πn

Combinar toda las soluciones

x = arcsin (\frac{15}{17}) + 2 πn, x = π - arcsin (\frac{15}{17}) + 2 πn, x = arcsin (- \frac{15}{17}) + 2 πn, x = π + arcsin (\frac{15}{17}) + 2 πn

Mostrar soluciones en forma decimal

x = 1.22069 \dots + 2 πn, x = π - 1.22069 \dots + 2 πn, x = - 1.22069 \dots + 2 πn, x = π + 1.22069 \dots + 2 πn

Ejemplos populares

cos(x)=53

cos (x) = 53

sin^2(a)=(1-cos(a))/2

sin^{2} (a) = \frac{1 - cos ( a )}{2}

cos(x)=(-11)/(12)

cos (x) = \frac{- 11}{12}

6sin^2(x)+5cos(x)-2=0

6 sin^{2} (x) + 5 cos (x) - 2 = 0

(sin^{22}(a))/(sin^2(a))=4-4sin^2(a)

\frac{sin ^{22} ( a )}{sin ^{2} ( a )} = 4 - 4 sin^{2} (a)