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Popular >

sin^2(x)+tan^2(x)=0

Solución

sin^{2} (x) + tan^{2} (x) = 0

Solución

x = 2 πn, x = π + 2 πn

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

sin^{2} (x) + tan^{2} (x) = 0

Expresar con seno, coseno

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

Utilizar la identidad trigonométrica básica:

tan (x) = \frac{sin ( x )}{cos ( x )}

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

Simplificar

sin^{2} (x) + (\frac{sin ( x )}{cos ( x )})^{2} : \frac{sin ^{2} ( x ) cos ^{2} ( x ) + sin ^{2} ( x )}{cos ^{2} ( x )}

sin^{2} (x) + (\frac{sin ( x )}{cos ( x )})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Convertir a fracción:

sin^{2} (x) = \frac{sin ^{2} ( x ) cos ^{2} ( x )}{cos ^{2} ( x )}

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

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

\frac{sin ^{2} ( x ) + cos ^{2} ( x ) sin ^{2} ( x )}{cos ^{2} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Factorizar

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

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

Factorizar el termino común

sin^{2} (x)

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

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

Resolver cada parte por separado

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

sin^{2} (x) = 0 : x = 2 πn, x = π + 2 πn

sin^{2} (x) = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

Soluciones generales para

sin (x) = 0

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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 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, x = π + 2 πn

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

Sin solución

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

Usando el método de sustitución

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

Sea:

cos (x) = u

u^{2} + 1 = 0

u^{2} + 1 = 0 : u = i, u = - i

u^{2} + 1 = 0

Mover

1

al lado derecho

u^{2} + 1 = 0

Restar

1

de ambos lados

u^{2} + 1 - 1 = 0 - 1

Simplificar

u^{2} = - 1

u^{2} = - 1

Para

x^{2} = f (a)

las soluciones son

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

u = - 1, u = - - 1

Simplificar

- 1 : i

- 1

Aplicar las propiedades de los numeros imaginarios:

- 1 = i

= i

Simplificar

- - 1 : - i

- - 1

Aplicar las propiedades de los numeros imaginarios:

- 1 = i

= - i

u = i, u = - i

Sustituir en la ecuación

u = cos (x)

cos (x) = i, cos (x) = - i

cos (x) = i, cos (x) = - i

cos (x) = i :

Sin solución

cos (x) = i

Sin soluci \overset{o}{ˊ} n

cos (x) = - i :

Sin solución

cos (x) = - i

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn

Ejemplos populares

tan(x)= 9/12

tan (x) = \frac{9}{12}

cos(x)= 24/25

cos (x) = \frac{24}{25}

2(tan(θ)+3)=5+tan(θ),0<= θ<2pi

2 (tan (θ) + 3) = 5 + tan (θ), 0 \leq θ < 2 π

3cos(3θ)=2cos(θ)

3 cos (3 θ) = 2 cos (θ)

(1-csc(θ))/(cot(θ))=tan(θ)-csc(θ)

\frac{1 - csc ( θ )}{cot ( θ )} = tan (θ) - csc (θ)