es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solución

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

Solución

x = \frac{π}{4} + πn

+1

Grados

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

Pasos de solución

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

Restar

2 cos (x)

de ambos lados

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

Sumar

2

a 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(x)+sin(x)=(sqrt(6))/2

cos (x) + sin (x) = \frac{6}{2}

6 tan^{2} (x) - 2 = 0

tan(x)=infinity

tan (x) = \infty

2arctanh(((x-2))/((x+1)))=ln(2)

2 arctanh (\frac{( x - 2 )}{( x + 1 )}) = ln (2)

tan (x) = - 1.5