English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solución

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

x = 1.37340 \dots + πn

Grados

x = 78.69006 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Restar

2 (sin (x) + cos (x))

de ambos lados

sin (x) - 5 cos (x) = 0

Re-escribir usando identidades trigonométricas

sin (x) - 5 cos (x) = 0

Dividir ambos lados entre

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

\frac{sin ( x ) - 5 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplificar

\frac{sin ( x )}{cos ( x )} - 5 = 0

Utilizar la identidad trigonométrica básica:

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

tan (x) - 5 = 0

tan (x) - 5 = 0

Mover

5

al lado derecho

tan (x) - 5 = 0

Sumar

5

a ambos lados

tan (x) - 5 + 5 = 0 + 5

Simplificar

tan (x) = 5

tan (x) = 5

Aplicar propiedades trigonométricas inversas

tan (x) = 5

Soluciones generales para

tan (x) = 5

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (5) + πn

x = arctan (5) + πn

Mostrar soluciones en forma decimal

x = 1.37340 \dots + πn

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

θ, ma = t sin (θ) - m g

x, sin (x) - cos (y) - 2 = 0

\frac{cot ( a )}{cos ( a )} = cos (a)

cos (x) - 2 = 0