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Popular >

-cos(2x)=2cos(2x)-1

Solución

- cos (2 x) = 2 cos (2 x) - 1

Solución

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

+1

Grados

x = 35.26438 \dots^{\circ} + 18 0^{\circ} n, x = 144.73561 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

- cos (2 x) = 2 cos (2 x) - 1

Usando el método de sustitución

- cos (2 x) = 2 cos (2 x) - 1

Sea:

cos (2 x) = u

- u = 2 u - 1

- u = 2 u - 1 : u = \frac{1}{3}

- u = 2 u - 1

Mover

2 u

al lado izquierdo

- u = 2 u - 1

Restar

2 u

de ambos lados

- u - 2 u = 2 u - 1 - 2 u

Simplificar

- 3 u = - 1

- 3 u = - 1

Dividir ambos lados entre

- 3

- 3 u = - 1

Dividir ambos lados entre

- 3

\frac{- 3 u}{- 3} = \frac{- 1}{- 3}

Simplificar

u = \frac{1}{3}

u = \frac{1}{3}

Sustituir en la ecuación

u = cos (2 x)

cos (2 x) = \frac{1}{3}

cos (2 x) = \frac{1}{3}

cos (2 x) = \frac{1}{3} : x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

cos (2 x) = \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cos (2 x) = \frac{1}{3}

Soluciones generales para

cos (2 x) = \frac{1}{3}

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

2 x = arccos (\frac{1}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

2 x = arccos (\frac{1}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

Resolver

2 x = arccos (\frac{1}{3}) + 2 πn : x = \frac{arccos ( \frac{1}{3} )}{2} + πn

2 x = arccos (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

2 x = arccos (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arccos ( \frac{1}{3} )}{2} + πn

x = \frac{arccos ( \frac{1}{3} )}{2} + πn

Resolver

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn : x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

Simplificar

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

Combinar toda las soluciones

x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

Mostrar soluciones en forma decimal

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

Ejemplos populares

sin(x)=2sqrt(3)

sin (x) = 23

sin(A)=(sqrt(3))/2

sin (A) = \frac{3}{2}

sin(θ)= 3/5 ,tan(θ)

sin (θ) = \frac{3}{5}, tan (θ)

sin^{22}(x)=0.5

sin^{22} (x) = 0.5

arctan(z)= pi/2

arctan (z) = \frac{π}{2}