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solvefor x,d^2+3d+2y=4cos^2(x)

Solución

resolver para

x, d^{2} + 3 d + 2 y = 4 cos^{2} (x)

Solución

x = arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

Pasos de solución

d^{2} + 3 d + 2 y = 4 cos^{2} (x)

Intercambiar lados

4 cos^{2} (x) = d^{2} + 3 d + 2 y

Usando el método de sustitución

4 cos^{2} (x) = d^{2} + 3 d + 2 y

Sea:

cos (x) = u

4 u^{2} = d^{2} + 3 d + 2 y

4 u^{2} = d^{2} + 3 d + 2 y : u = \frac{d ^{2} + 3 d + 2 y}{2}, u = - \frac{d ^{2} + 3 d + 2 y}{2}

4 u^{2} = d^{2} + 3 d + 2 y

Dividir ambos lados entre

4

4 u^{2} = d^{2} + 3 d + 2 y

Dividir ambos lados entre

4

\frac{4 u ^{2}}{4} = \frac{d ^{2}}{4} + \frac{3 d}{4} + \frac{2 y}{4}

Simplificar

\frac{4 u ^{2}}{4} = \frac{d ^{2}}{4} + \frac{3 d}{4} + \frac{2 y}{4}

Simplificar

\frac{4 u ^{2}}{4} : u^{2}

\frac{4 u ^{2}}{4}

Dividir:

\frac{4}{4} = 1

= u^{2}

Simplificar

\frac{d ^{2}}{4} + \frac{3 d}{4} + \frac{2 y}{4} : \frac{d ^{2} + 3 d + 2 y}{4}

\frac{d ^{2}}{4} + \frac{3 d}{4} + \frac{2 y}{4}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{d ^{2} + 3 d + 2 y}{4}

u^{2} = \frac{d ^{2} + 3 d + 2 y}{4}

u^{2} = \frac{d ^{2} + 3 d + 2 y}{4}

u^{2} = \frac{d ^{2} + 3 d + 2 y}{4}

Para

x^{2} = f (a)

las soluciones son

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

u = \frac{d ^{2} + 3 d + 2 y}{4}, u = - \frac{d ^{2} + 3 d + 2 y}{4}

Simplificar

\frac{d ^{2} + 3 d + 2 y}{4} : \frac{d ^{2} + 3 d + 2 y}{2}

\frac{d ^{2} + 3 d + 2 y}{4}

Aplicar la siguiente propiedad de los radicales:

asumiendo que

a \geq 0, b \geq 0

= \frac{d ^{2} + 3 d + 2 y}{4}

4 = 2

4

Descomponer el número en factores primos:

4 = 2^{2}

= 2^{2}

Aplicar las leyes de los exponentes:

2^{2} = 2

= 2

= \frac{d ^{2} + 3 d + 2 y}{2}

Simplificar

- \frac{d ^{2} + 3 d + 2 y}{4} : - \frac{d ^{2} + 3 d + 2 y}{2}

- \frac{d ^{2} + 3 d + 2 y}{4}

Simplificar

\frac{d ^{2} + 3 d + 2 y}{4} : \frac{d ^{2} + 3 d + 2 y}{2}

\frac{d ^{2} + 3 d + 2 y}{4}

Aplicar la siguiente propiedad de los radicales:

asumiendo que

a \geq 0, b \geq 0

= \frac{d ^{2} + 3 d + 2 y}{4}

4 = 2

4

Descomponer el número en factores primos:

4 = 2^{2}

= 2^{2}

Aplicar las leyes de los exponentes:

2^{2} = 2

= 2

= \frac{d ^{2} + 3 d + 2 y}{2}

= - \frac{2 y + d ^{2} + 3 d}{2}

= - \frac{d ^{2} + 3 d + 2 y}{2}

u = \frac{d ^{2} + 3 d + 2 y}{2}, u = - \frac{d ^{2} + 3 d + 2 y}{2}

Sustituir en la ecuación

u = cos (x)

cos (x) = \frac{d ^{2} + 3 d + 2 y}{2}, cos (x) = - \frac{d ^{2} + 3 d + 2 y}{2}

cos (x) = \frac{d ^{2} + 3 d + 2 y}{2}, cos (x) = - \frac{d ^{2} + 3 d + 2 y}{2}

cos (x) = \frac{d ^{2} + 3 d + 2 y}{2} : x = arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

cos (x) = \frac{d ^{2} + 3 d + 2 y}{2}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{d ^{2} + 3 d + 2 y}{2}

Soluciones generales para

cos (x) = \frac{d ^{2} + 3 d + 2 y}{2}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

x = arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

cos (x) = - \frac{d ^{2} + 3 d + 2 y}{2} : x = arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

cos (x) = - \frac{d ^{2} + 3 d + 2 y}{2}

Aplicar propiedades trigonométricas inversas

cos (x) = - \frac{d ^{2} + 3 d + 2 y}{2}

Soluciones generales para

cos (x) = - \frac{d ^{2} + 3 d + 2 y}{2}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

x = arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

Combinar toda las soluciones

x = arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (\frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn, x = - arccos (- \frac{d ^{2} + 3 d + 2 y}{2}) + 2 πn

Ejemplos populares

(1+tan^2(x))cos^2(x)=sec(x)

(1 + tan^{2} (x)) cos^{2} (x) = sec (x)

(cos^2(x)-1)/(sin^2(x))=-tan(x)

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

cos^6(x)=-cos^2(x)

cos^{6} (x) = - cos^{2} (x)

2sin^3(x)-5sin^2(x)+2sin(x)=0

2 sin^{3} (x) - 5 sin^{2} (x) + 2 sin (x) = 0

(cos^2(a)-3cos(a)+2)/(sin^2(a))=1

\frac{cos ^{2} ( a ) - 3 cos ( a ) + 2}{sin ^{2} ( a )} = 1