English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cos(x)-sin(x))/(cos(x))=tan(x)-1

Solución

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

Solución

x = \frac{π}{4} + πn

Grados

x = 4 5^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Restar

tan (x) - 1

de ambos lados

\frac{cos ( x ) - sin ( x )}{cos ( x )} - tan (x) + 1 = 0

Simplificar

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

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

Convertir a fracción:

tan (x) = \frac{tan ( x ) cos ( x )}{cos ( x )}, 1 = \frac{1 cos ( x )}{cos ( x )}

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

Sumar elementos similares:

cos (x) + 1 \cdot cos (x) = 2 cos (x)

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

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

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

2 cos (x) - sin (x) - tan (x) cos (x) = 0

Re-escribir usando identidades trigonométricas

- sin (x) + 2 cos (x) - cos (x) tan (x)

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

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

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

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

cos (x)

= sin (x)

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

Sumar elementos similares:

- sin (x) - sin (x) = - 2 sin (x)

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

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

Dividir ambos lados entre

cos (x), cos (x) \neq = 0

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

2 - 2 tan (x) = 0

2 - 2 tan (x) = 0

Mover

2

al lado derecho

2 - 2 tan (x) = 0

Restar

2

de ambos lados

2 - 2 tan (x) - 2 = 0 - 2

Simplificar

- 2 tan (x) = - 2

- 2 tan (x) = - 2

Dividir ambos lados entre

- 2

- 2 tan (x) = - 2

Dividir ambos lados entre

- 2

\frac{- 2 tan ( x )}{- 2} = \frac{- 2}{- 2}

Simplificar

tan (x) = 1

tan (x) = 1

Soluciones generales para

tan (x) = 1

tan (x)

tabla de valores periódicos con

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Ejemplos populares

cos(φ)= 1/4

cos (φ) = \frac{1}{4}

-2cos(x)=sin(x)

- 2 cos (x) = sin (x)

sin(x)=-0.9781

sin (x) = - 0.9781

tan(x)=3.73

tan (x) = 3.73

tan(θ)=-2/5 ,sin(θ)>0

tan (θ) = - \frac{2}{5}, sin (θ) > 0