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Popular >

1-(cos^2(x))/(1+sin(x))=2cos(x)

Solución

1 - \frac{cos ^{2} ( x )}{1 + sin ( x )} = 2 cos (x)

Solución

x = 1.10714 \dots + πn

Grados

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

1 - \frac{cos ^{2} ( x )}{1 + sin ( x )} = 2 cos (x)

Restar

2 cos (x)

de ambos lados

1 - \frac{cos ^{2} ( x )}{1 + sin ( x )} - 2 cos (x) = 0

Simplificar

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

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

Convertir a fracción:

1 = \frac{1 ( 1 + sin ( x ) )}{1 + sin ( x )}, 2 cos (x) = \frac{2 cos ( x ) ( 1 + sin ( x ) )}{1 + sin ( x )}

= \frac{1 \cdot ( 1 + sin ( x ) )}{1 + sin ( x )} - \frac{cos ^{2} ( x )}{1 + sin ( x )} - \frac{2 cos ( x ) ( 1 + sin ( x ) )}{1 + sin ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot ( 1 + sin ( x ) ) - cos ^{2} ( x ) - 2 cos ( x ) ( 1 + sin ( x ) )}{1 + sin ( x )}

1 \cdot (1 + sin (x)) = 1 + sin (x)

1 \cdot (1 + sin (x))

Multiplicar:

1 \cdot (1 + sin (x)) = (1 + sin (x))

= (1 + sin (x))

Quitar los parentesis:

(a) = a

= 1 + sin (x)

= \frac{1 + sin ( x ) - cos ^{2} ( x ) - 2 cos ( x ) ( sin ( x ) + 1 )}{1 + sin ( x )}

\frac{1 + sin ( x ) - cos ^{2} ( x ) - 2 cos ( x ) ( 1 + sin ( x ) )}{1 + sin ( x )} = 0

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

1 + sin (x) - cos^{2} (x) - 2 cos (x) (1 + sin (x)) = 0

Re-escribir usando identidades trigonométricas

1 - cos^{2} (x) + sin (x) - (1 + sin (x)) \cdot 2 cos (x)

Utilizar la identidad pitagórica:

1 = cos^{2} (x) + sin^{2} (x)

1 - cos^{2} (x) = sin^{2} (x)

= sin (x) - 2 cos (x) (1 + sin (x)) + sin^{2} (x)

sin (x) + sin^{2} (x) - (1 + sin (x)) \cdot 2 cos (x) = 0

Factorizar

sin (x) + sin^{2} (x) - (1 + sin (x)) \cdot 2 cos (x) : (1 + sin (x)) (sin (x) - 2 cos (x))

sin (x) + sin^{2} (x) - (1 + sin (x)) \cdot 2 cos (x)

Aplicar las leyes de los exponentes:

a^{b + c} = a^{b} a^{c}

sin^{2} (x) = sin (x) sin (x)

= sin (x) + sin (x) sin (x) - 2 (1 + sin (x)) cos (x)

Factorizar el termino común

sin (x)

= sin (x) (1 + sin (x)) - 2 (1 + sin (x)) cos (x)

Factorizar el termino común

(1 + sin (x))

= (1 + sin (x)) (sin (x) - 2 cos (x))

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

Resolver cada parte por separado

1 + sin (x) = 0 or sin (x) - 2 cos (x) = 0

1 + sin (x) = 0 : x = \frac{3 π}{2} + 2 πn

1 + sin (x) = 0

Mover

1

al lado derecho

1 + sin (x) = 0

Restar

1

de ambos lados

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

Simplificar

sin (x) = - 1

sin (x) = - 1

Soluciones generales para

sin (x) = - 1

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 = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

sin (x) - 2 cos (x) = 0 : x = arctan (2) + πn

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

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

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

tan (x) - 2 = 0

tan (x) - 2 = 0

Mover

2

al lado derecho

tan (x) - 2 = 0

Sumar

2

a ambos lados

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

Simplificar

tan (x) = 2

tan (x) = 2

Aplicar propiedades trigonométricas inversas

tan (x) = 2

Soluciones generales para

tan (x) = 2

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

x = arctan (2) + πn

x = arctan (2) + πn

Combinar toda las soluciones

x = \frac{3 π}{2} + 2 πn, x = arctan (2) + πn

Siendo que la ecuación esta indefinida para:

\frac{3 π}{2} + 2 πn

x = arctan (2) + πn

Mostrar soluciones en forma decimal

x = 1.10714 \dots + πn

Ejemplos populares

cos(x)= 4/14

cos (x) = \frac{4}{14}

(sin(57.22))/(31.5)=(sin(θ))/(24.4)

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( θ )}{24.4}

tan^2(b)sin^2(b)=tan^2(b)+sin^2(b)

tan^{2} (b) sin^{2} (b) = tan^{2} (b) + sin^{2} (b)

cos(2θ)=(sqrt(3))/2 ,0<= θ<2pi

cos (2 θ) = \frac{3}{2}, 0 \leq θ < 2 π

7.5sin(x)=3.4cos(x)

7.5 sin (x) = 3.4 cos (x)