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2cos^4(x)cos(x)-cos^5(x)=1

Solución

2 cos^{4} (x) cos (x) - cos^{5} (x) = 1

Solución

x = 2 πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n

Pasos de solución

2 cos^{4} (x) cos (x) - cos^{5} (x) = 1

Simplificar

2 cos^{4} (x) cos (x) - cos^{5} (x) : cos^{5} (x)

2 cos^{4} (x) cos (x) - cos^{5} (x)

2 cos^{4} (x) cos (x) = 2 cos^{5} (x)

2 cos^{4} (x) cos (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cos^{4} (x) cos (x) = cos^{4 + 1} (x)

= 2 cos^{4 + 1} (x)

Sumar:

4 + 1 = 5

= 2 cos^{5} (x)

= 2 cos^{5} (x) - cos^{5} (x)

Sumar elementos similares:

2 cos^{5} (x) - cos^{5} (x) = cos^{5} (x)

= cos^{5} (x)

cos^{5} (x) = 1

Para

x^{n} = f (a)

, n es impar, la solución es

Aplicar la regla

= 1

cos (x) = 1

Soluciones generales para

cos (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Ejemplos populares

cos^4(x)-2sin^2(x)-1=0

cos^{4} (x) - 2 sin^{2} (x) - 1 = 0

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d^{2} (1 + cos (x)) - (1 + cos (x))^{2} = sin^{2} (x)

cos^4(x)-2cos^2(x)+1=0

cos^{4} (x) - 2 cos^{2} (x) + 1 = 0

sin^2(x)+cos^2(x)+cos(x)=2

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

(sin^3(x))/(sin(x))=0

\frac{sin ^{3} ( x )}{sin ( x )} = 0