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cos(pi+x)+cos(pi+x)=1

Solución

cos (π + x) + cos (π + x) = 1

Solución

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

+1

Grados

x = - 12 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Pasos de solución

cos (π + x) + cos (π + x) = 1

Simplificar

cos (π + x) + cos (π + x) : 2 cos (π + x)

cos (π + x) + cos (π + x)

Sumar elementos similares:

cos (x + π) + cos (x + π) = 2 cos (x + π)

= 2 cos (x + π)

2 cos (π + x) = 1

Dividir ambos lados entre

2

2 cos (π + x) = 1

Dividir ambos lados entre

2

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

Simplificar

cos (π + x) = \frac{1}{2}

cos (π + x) = \frac{1}{2}

Soluciones generales para

cos (π + 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}

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

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

Resolver

π + x = \frac{π}{3} + 2 πn : x = \frac{π}{3} + 2 πn - π

π + x = \frac{π}{3} + 2 πn

Mover

π

al lado derecho

π + x = \frac{π}{3} + 2 πn

Restar

π

de ambos lados

π + x - π = \frac{π}{3} + 2 πn - π

Simplificar

x = \frac{π}{3} + 2 πn - π

x = \frac{π}{3} + 2 πn - π

Resolver

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

π + x = \frac{5 π}{3} + 2 πn

Mover

π

al lado derecho

π + x = \frac{5 π}{3} + 2 πn

Restar

π

de ambos lados

π + x - π = \frac{5 π}{3} + 2 πn - π

Simplificar

x = \frac{5 π}{3} + 2 πn - π

x = \frac{5 π}{3} + 2 πn - π

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

Ejemplos populares

1 + 2 sin (θ) = 0

solvefor x,z=arcsin(xy)resolver para

x, z = arcsin (x y)

2 cos (x) - 2 = 0

4sin^2(θ)-13sin(θ)+9=0

4 sin^{2} (θ) - 13 sin (θ) + 9 = 0

2sqrt(3)cos^2(x)=sin(x)

23 cos^{2} (x) = sin (x)