English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x)= 1/(sec(x))

Solución

tan (x) = \frac{1}{sec ( x )}

Solución

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Grados

x = 38.17270 \dots^{\circ} + 36 0^{\circ} n, x = 141.82729 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

tan (x) = \frac{1}{sec ( x )}

Restar

\frac{1}{sec ( x )}

de ambos lados

tan (x) - \frac{1}{sec ( x )} = 0

Simplificar

tan (x) - \frac{1}{sec ( x )} : \frac{tan ( x ) sec ( x ) - 1}{sec ( x )}

tan (x) - \frac{1}{sec ( x )}

Convertir a fracción:

tan (x) = \frac{tan ( x ) sec ( x )}{sec ( x )}

= \frac{tan ( x ) sec ( x )}{sec ( x )} - \frac{1}{sec ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{tan ( x ) sec ( x ) - 1}{sec ( x )}

\frac{tan ( x ) sec ( x ) - 1}{sec ( x )} = 0

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

tan (x) sec (x) - 1 = 0

Expresar con seno, coseno

- 1 + sec (x) tan (x)

Utilizar la identidad trigonométrica básica:

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

= - 1 + \frac{1}{cos ( x )} tan (x)

Utilizar la identidad trigonométrica básica:

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

= - 1 + \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Simplificar

- 1 + \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )} : \frac{- cos ^{2} ( x ) + sin ( x )}{cos ^{2} ( x )}

- 1 + \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )} = \frac{sin ( x )}{cos ^{2} ( x )}

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiplicar fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot sin ( x )}{cos ( x ) cos ( x )}

Multiplicar:

1 \cdot sin (x) = sin (x)

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

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

cos (x) cos (x)

Aplicar las leyes de los exponentes:

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

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

= cos^{1 + 1} (x)

Sumar:

1 + 1 = 2

= cos^{2} (x)

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

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

Convertir a fracción:

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

= - \frac{1 \cdot cos ^{2} ( x )}{cos ^{2} ( x )} + \frac{sin ( 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{- 1 \cdot cos ^{2} ( x ) + sin ( x )}{cos ^{2} ( x )}

Multiplicar:

1 \cdot cos^{2} (x) = cos^{2} (x)

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

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

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

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

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad pitagórica:

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

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

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

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

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

Poner los parentesis

= - (1) - (- sin^{2} (x))

Aplicar las reglas de los signos

- (- a) = a, - (a) = - a

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

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

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

Usando el método de sustitución

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

Sea:

sin (x) = u

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

- 1 + u + u^{2} = 0 : u = \frac{- 1 + 5}{2}, u = \frac{- 1 - 5}{2}

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

Escribir en la forma binómica

a x^{2} + b x + c = 0

u^{2} + u - 1 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

u^{2} + u - 1 = 0

Formula general para ecuaciones de segundo grado:

Para

a = 1, b = 1, c = - 1

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 1) = 5

1^{2} - 4 \cdot 1 \cdot (- 1)

Aplicar la regla

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 1 \cdot (- 1)

Aplicar la regla

- (- a) = a

= 1 + 4 \cdot 1 \cdot 1

Multiplicar los numeros:

4 \cdot 1 \cdot 1 = 4

= 1 + 4

Sumar:

1 + 4 = 5

= 5

u_{1, 2} = \frac{- 1 \pm 5}{2 \cdot 1}

Separar las soluciones

u_{1} = \frac{- 1 + 5}{2 \cdot 1}, u_{2} = \frac{- 1 - 5}{2 \cdot 1}

u = \frac{- 1 + 5}{2 \cdot 1} : \frac{- 1 + 5}{2}

\frac{- 1 + 5}{2 \cdot 1}

Multiplicar los numeros:

2 \cdot 1 = 2

= \frac{- 1 + 5}{2}

u = \frac{- 1 - 5}{2 \cdot 1} : \frac{- 1 - 5}{2}

\frac{- 1 - 5}{2 \cdot 1}

Multiplicar los numeros:

2 \cdot 1 = 2

= \frac{- 1 - 5}{2}

Las soluciones a la ecuación de segundo grado son:

u = \frac{- 1 + 5}{2}, u = \frac{- 1 - 5}{2}

Sustituir en la ecuación

u = sin (x)

sin (x) = \frac{- 1 + 5}{2}, sin (x) = \frac{- 1 - 5}{2}

sin (x) = \frac{- 1 + 5}{2}, sin (x) = \frac{- 1 - 5}{2}

sin (x) = \frac{- 1 + 5}{2} : x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

sin (x) = \frac{- 1 + 5}{2}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{- 1 + 5}{2}

Soluciones generales para

sin (x) = \frac{- 1 + 5}{2}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

sin (x) = \frac{- 1 - 5}{2} :

Sin solución

sin (x) = \frac{- 1 - 5}{2}

- 1 \leq sin (x) \leq 1

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Ejemplos populares

2*cos(2x)-1=0

2 \cdot cos (2 x) - 1 = 0

sin^2(x)=((7m-2))/8

sin^{2} (x) = \frac{( 7 m - 2 )}{8}

cos(θ)+sqrt(2)=0

cos (θ) + 2 = 0

2sec(x)=sqrt(2)tan(x)+3sec(x)

2 sec (x) = 2 tan (x) + 3 sec (x)

4cos(x)+3sin(x)=5

4 cos (x) + 3 sin (x) = 5