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Popular >

1+cos^2(x^2+1)=sin^2(x^2+1)

Solución

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

Solución

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

Grados

x = 0^{\circ} + 110.39499 \dots^{\circ} n, x = 0^{\circ} - 110.39499 \dots^{\circ} n

Pasos de solución

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

Restar

sin^{2} (x^{2} + 1)

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad trigonométrica del ángulo doble:

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

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

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

Mover

1

al lado derecho

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

Restar

1

de ambos lados

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

Simplificar

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

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

Soluciones generales para

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

2 (1 + x^{2}) = π + 2 πn

2 (1 + x^{2}) = π + 2 πn

Resolver

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

2 (1 + x^{2}) = π + 2 πn

Dividir ambos lados entre

2

2 (1 + x^{2}) = π + 2 πn

Dividir ambos lados entre

2

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

Simplificar

1 + x^{2} = \frac{π}{2} + πn

1 + x^{2} = \frac{π}{2} + πn

Mover

1

al lado derecho

1 + x^{2} = \frac{π}{2} + πn

Restar

1

de ambos lados

1 + x^{2} - 1 = \frac{π}{2} + πn - 1

Simplificar

x^{2} = \frac{π}{2} + πn - 1

x^{2} = \frac{π}{2} + πn - 1

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

x = \frac{π}{2} + πn - 1, x = - \frac{π}{2} + πn - 1

Simplificar

\frac{π}{2} + πn - 1 : \frac{π + 2 πn - 2}{2}

\frac{π}{2} + πn - 1

Simplificar

\frac{π}{2} + πn - 1

en una fracción:

\frac{π + 2 πn - 2}{2}

\frac{π}{2} + πn - 1

Convertir a fracción:

πn = \frac{πn 2}{2}, 1 = \frac{1 \cdot 2}{2}

= \frac{π}{2} + \frac{πn \cdot 2}{2} - \frac{1 \cdot 2}{2}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{π + πn \cdot 2 - 1 \cdot 2}{2}

Multiplicar los numeros:

1 \cdot 2 = 2

= \frac{π + 2 πn - 2}{2}

= \frac{π + πn \cdot 2 - 2}{2}

= \frac{π + 2 πn - 2}{2}

Simplificar

- \frac{π}{2} + πn - 1 : - \frac{π + 2 πn - 2}{2}

- \frac{π}{2} + πn - 1

Simplificar

\frac{π}{2} + πn - 1

en una fracción:

\frac{π + 2 πn - 2}{2}

\frac{π}{2} + πn - 1

Convertir a fracción:

πn = \frac{πn 2}{2}, 1 = \frac{1 \cdot 2}{2}

= \frac{π}{2} + \frac{πn \cdot 2}{2} - \frac{1 \cdot 2}{2}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{π + πn \cdot 2 - 1 \cdot 2}{2}

Multiplicar los numeros:

1 \cdot 2 = 2

= \frac{π + 2 πn - 2}{2}

= - \frac{π + 2 πn - 2}{2}

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

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

Ejemplos populares

2sin^2(x)+sin(x)-6=0

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tan(θ)= 8/15 ,sin(θ)>0

tan (θ) = \frac{8}{15}, sin (θ) > 0

cos(x)=(86.6)/(100)

cos (x) = \frac{86.6}{100}

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-6sin(θ)=-3sqrt(3)

- 6 sin (θ) = - 33