English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

([sin(x)+cos(x)])/(cos(x))=sin(x)+1

Solución

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

x = 2 πn, x = π + 2 πn

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Restar

sin (x) + 1

de ambos lados

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

Simplificar

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

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

Convertir a fracción:

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

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

Sumar elementos similares:

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

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

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

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

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

Factorizar

sin (x) - sin (x) cos (x) : - sin (x) (cos (x) - 1)

sin (x) - sin (x) cos (x)

Factorizar el termino común

- sin (x)

= - sin (x) (- 1 + cos (x))

- sin (x) (cos (x) - 1) = 0

Resolver cada parte por separado

sin (x) = 0 or cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

Soluciones generales para

sin (x) = 0

tabla de valores periódicos con

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

cos (x) - 1 = 0

Mover

1

al lado derecho

cos (x) - 1 = 0

Sumar

1

a ambos lados

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

Simplificar

cos (x) = 1

cos (x) = 1

Soluciones generales para

cos (x) = 1

cos (x)

tabla de valores periódicos con

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn

cos (A) = 0.4639

csc (A) = \frac{9.43}{5}

cos (x) cos (3 5^{\circ}) = 1 - sin (x) sin (3 5^{\circ})

4 sin^{2} (x) + 2 sin (x) = 2, 0 \leq x \leq 2 π

3 tan (\frac{1}{3} x) = 8