es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solución

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

Solución

x = \frac{3 π}{4} + πn

+1

Grados

x = 13 5^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Restar

tan (x) cos (x) - cos (x)

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

cos (x) + 2 sin (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)

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

Sumar elementos similares:

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

= cos (x) + sin (x)

= cos (x) + sin (x)

Dividir ambos lados entre

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

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

1 + tan (x) = 0

1 + tan (x) = 0

Mover

1

al lado derecho

1 + tan (x) = 0

Restar

1

de ambos lados

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

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

Ejemplos populares

solvefor x,z=3-sin(2x+y)resolver para

x, z = 3 - sin (2 x + y)

tan (x) = \frac{27}{48}

cos(θ)-sin(θ)=1,0<= θ<= 2pi

cos (θ) - sin (θ) = 1, 0 \leq θ \leq 2 π

2 cos (x) = - 0.2

cot(θ-pi/2)=1.07

cot (θ - \frac{π}{2}) = 1.07