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Popular >

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

Solución

e^{2 c o s (x) - 1} = 1

Solución

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

Grados

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Pasos de solución

e^{2 c o s (x) - 1} = 1

Aplicar las leyes de los exponentes

e^{2 c o s (x) - 1} = 1

Si

f (x) = g (x)

, entonces

ln (f (x)) = ln (g (x))

ln (e^{2 c o s (x) - 1}) = ln (1)

Aplicar las propiedades de los logaritmos:

ln (e^{a}) = a

ln (e^{2 c o s (x) - 1}) = 2 cos (x) - 1

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

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

Resolver

2 cos (x) - 1 = ln (1) : cos (x) = \frac{1}{2}

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

Mover

1

al lado derecho

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

Sumar

1

a ambos lados

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

Simplificar

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

Simplificar

2 cos (x) - 1 + 1 : 2 cos (x)

2 cos (x) - 1 + 1

Sumar elementos similares:

- 1 + 1 = 0

= 2 cos (x)

Simplificar

ln (1) + 1 : 1

ln (1) + 1

Aplicar las propiedades de los logaritmos:

lo g_{a} (1) = 0

= 0 + 1

Simplificar

= 1

2 cos (x) = 1

2 cos (x) = 1

2 cos (x) = 1

Dividir ambos lados entre

2

2 cos (x) = 1

Dividir ambos lados entre

2

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

Simplificar

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

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

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

Soluciones generales para

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

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Ejemplos populares

csc(θ)=-37/12 ,(3pi)/2 <= θ<= 2pi

csc (θ) = - \frac{37}{12}, \frac{3 π}{2} \leq θ \leq 2 π

3/2 =2*25sin(θ/2)

\frac{3}{2} = 2 \cdot 25 sin (\frac{θ}{2})

sin^2(x)-sin(x)-12=0

sin^{2} (x) - sin (x) - 12 = 0

7sin(2ϕ)+12cos(ϕ)=0

7 sin (2 ϕ) + 12 cos (ϕ) = 0

sec(θ/2)=cos(θ/2)

sec (\frac{θ}{2}) = cos (\frac{θ}{2})