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Popular >

solvefor x,e^ycos(2x)+y=1

Solución

resolver para

x, e^{y} cos (2 x) + y = 1

Solución

x = \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn, x = - \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

Pasos de solución

e^{y} cos (2 x) + y = 1

Mover

y

al lado derecho

e^{y} cos (2 x) + y = 1

Restar

y

de ambos lados

e^{y} cos (2 x) + y - y = 1 - y

Simplificar

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

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

Dividir ambos lados entre

e^{y}

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

Dividir ambos lados entre

e^{y}

\frac{e ^{y} cos ( 2 x )}{e ^{y}} = \frac{1}{e ^{y}} - \frac{y}{e ^{y}}

Simplificar

\frac{e ^{y} cos ( 2 x )}{e ^{y}} = \frac{1}{e ^{y}} - \frac{y}{e ^{y}}

Simplificar

\frac{e ^{y} cos ( 2 x )}{e ^{y}} : cos (2 x)

\frac{e ^{y} cos ( 2 x )}{e ^{y}}

Eliminar los terminos comunes:

e^{y}

= cos (2 x)

Simplificar

\frac{1}{e ^{y}} - \frac{y}{e ^{y}} : \frac{1 - y}{e ^{y}}

\frac{1}{e ^{y}} - \frac{y}{e ^{y}}

Aplicar la regla

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

= \frac{1 - y}{e ^{y}}

cos (2 x) = \frac{1 - y}{e ^{y}}

cos (2 x) = \frac{1 - y}{e ^{y}}

cos (2 x) = \frac{1 - y}{e ^{y}}

Aplicar propiedades trigonométricas inversas

cos (2 x) = \frac{1 - y}{e ^{y}}

Soluciones generales para

cos (2 x) = \frac{1 - y}{e ^{y}}

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

2 x = arccos (\frac{1 - y}{e ^{y}}) + 2 πn, 2 x = - arccos (\frac{1 - y}{e ^{y}}) + 2 πn

2 x = arccos (\frac{1 - y}{e ^{y}}) + 2 πn, 2 x = - arccos (\frac{1 - y}{e ^{y}}) + 2 πn

Resolver

2 x = arccos (\frac{1 - y}{e ^{y}}) + 2 πn : x = \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

2 x = arccos (\frac{1 - y}{e ^{y}}) + 2 πn

Dividir ambos lados entre

2

2 x = arccos (\frac{1 - y}{e ^{y}}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

x = \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

Resolver

2 x = - arccos (\frac{1 - y}{e ^{y}}) + 2 πn : x = - \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

2 x = - arccos (\frac{1 - y}{e ^{y}}) + 2 πn

Dividir ambos lados entre

2

2 x = - arccos (\frac{1 - y}{e ^{y}}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = - \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + \frac{2 πn}{2}

Simplificar

x = - \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

x = - \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

x = \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn, x = - \frac{arccos ( \frac{1 - y}{e ^{y}} )}{2} + πn

Ejemplos populares

cos(θ)=0.4,sec(θ)

cos (θ) = 0.4, sec (θ)

-pi/2 sin((pix)/2)=0

- \frac{π}{2} sin (\frac{π x}{2}) = 0

cot(θ)=(1+cos^2(θ))/(2sin(θ)cos(θ))

cot (θ) = \frac{1 + cos ^{2} ( θ )}{2 sin ( θ ) cos ( θ )}

cot(x)=sqrt(3)+1

cot (x) = 3 + 1

sec(3x)-csc(30)=0,(x+35)/5

sec (3 x) - csc (3 0^{\circ}) = 0, \frac{x + 35}{5}