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Popular >

sin^2(x)=8cos^2(x)

Solución

sin^{2} (x) = 8 cos^{2} (x)

Solución

x = - 1.23095 \dots + πn, x = 1.23095 \dots + πn

Grados

x = - 70.52877 \dots^{\circ} + 18 0^{\circ} n, x = 70.52877 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

sin^{2} (x) = 8 cos^{2} (x)

Restar

8 cos^{2} (x)

de ambos lados

sin^{2} (x) - 8 cos^{2} (x) = 0

Factorizar

sin^{2} (x) - 8 cos^{2} (x) : (sin (x) + 22 cos (x)) (sin (x) - 22 cos (x))

sin^{2} (x) - 8 cos^{2} (x)

Reescribir

sin^{2} (x) - 8 cos^{2} (x)

como

sin^{2} (x) - (8 cos (x))^{2}

sin^{2} (x) - 8 cos^{2} (x)

Aplicar las leyes de los exponentes:

a = (a)^{2}

8 = (8)^{2}

= sin^{2} (x) - (8)^{2} cos^{2} (x)

Aplicar las leyes de los exponentes:

a^{m} b^{m} = (ab)^{m}

(8)^{2} cos^{2} (x) = (8 cos (x))^{2}

= sin^{2} (x) - (8 cos (x))^{2}

= sin^{2} (x) - (8 cos (x))^{2}

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

sin^{2} (x) - (8 cos (x))^{2} = (sin (x) + 8 cos (x)) (sin (x) - 8 cos (x))

= (sin (x) + 8 cos (x)) (sin (x) - 8 cos (x))

Simplificar

= (sin (x) + 22 cos (x)) (sin (x) - 22 cos (x))

(sin (x) + 22 cos (x)) (sin (x) - 22 cos (x)) = 0

Resolver cada parte por separado

sin (x) + 22 cos (x) = 0 or sin (x) - 22 cos (x) = 0

sin (x) + 22 cos (x) = 0 : x = arctan (- 22) + πn

sin (x) + 22 cos (x) = 0

Re-escribir usando identidades trigonométricas

sin (x) + 22 cos (x) = 0

Dividir ambos lados entre

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

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

Simplificar

\frac{sin ( x )}{cos ( x )} + 22 = 0

Utilizar la identidad trigonométrica básica:

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

tan (x) + 22 = 0

tan (x) + 22 = 0

Mover

22

al lado derecho

tan (x) + 22 = 0

Restar

22

de ambos lados

tan (x) + 22 - 22 = 0 - 22

Simplificar

tan (x) = - 22

tan (x) = - 22

Aplicar propiedades trigonométricas inversas

tan (x) = - 22

Soluciones generales para

tan (x) = - 22

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

x = arctan (- 22) + πn

x = arctan (- 22) + πn

sin (x) - 22 cos (x) = 0 : x = arctan (22) + πn

sin (x) - 22 cos (x) = 0

Re-escribir usando identidades trigonométricas

sin (x) - 22 cos (x) = 0

Dividir ambos lados entre

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

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

Simplificar

\frac{sin ( x )}{cos ( x )} - 22 = 0

Utilizar la identidad trigonométrica básica:

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

tan (x) - 22 = 0

tan (x) - 22 = 0

Mover

22

al lado derecho

tan (x) - 22 = 0

Sumar

22

a ambos lados

tan (x) - 22 + 22 = 0 + 22

Simplificar

tan (x) = 22

tan (x) = 22

Aplicar propiedades trigonométricas inversas

tan (x) = 22

Soluciones generales para

tan (x) = 22

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

x = arctan (22) + πn

x = arctan (22) + πn

Combinar toda las soluciones

x = arctan (- 22) + πn, x = arctan (22) + πn

Mostrar soluciones en forma decimal

x = - 1.23095 \dots + πn, x = 1.23095 \dots + πn

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