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Popular >

cos^2(4x)-sin^2(4x)=cos(b)

Solución

cos^{2} (4 x) - sin^{2} (4 x) = cos (b)

x = \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}, x = - \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

Pasos de solución

cos^{2} (4 x) - sin^{2} (4 x) = cos (b)

Re-escribir usando identidades trigonométricas

cos^{2} (4 x) - sin^{2} (4 x)

Utilizar la identidad trigonométrica del ángulo doble:

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

= cos (2 \cdot 4 x)

cos (2 \cdot 4 x) = cos (b)

Aplicar propiedades trigonométricas inversas

cos (2 \cdot 4 x) = cos (b)

Soluciones generales para

cos (2 \cdot 4 x) = cos (b)

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

2 \cdot 4 x = arccos (cos (b)) + 2 πn, 2 \cdot 4 x = - arccos (cos (b)) + 2 πn

2 \cdot 4 x = arccos (cos (b)) + 2 πn, 2 \cdot 4 x = - arccos (cos (b)) + 2 πn

Resolver

2 \cdot 4 x = arccos (cos (b)) + 2 πn : x = \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

2 \cdot 4 x = arccos (cos (b)) + 2 πn

Dividir ambos lados entre

8

2 \cdot 4 x = arccos (cos (b)) + 2 πn

Dividir ambos lados entre

8

\frac{2 \cdot 4 x}{8} = \frac{arccos ( cos ( b ) )}{8} + \frac{2 πn}{8}

Simplificar

x = \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

x = \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

Resolver

2 \cdot 4 x = - arccos (cos (b)) + 2 πn : x = - \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

2 \cdot 4 x = - arccos (cos (b)) + 2 πn

Dividir ambos lados entre

8

2 \cdot 4 x = - arccos (cos (b)) + 2 πn

Dividir ambos lados entre

8

\frac{2 \cdot 4 x}{8} = - \frac{arccos ( cos ( b ) )}{8} + \frac{2 πn}{8}

Simplificar

x = - \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

x = - \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

x = \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}, x = - \frac{arccos ( cos ( b ) )}{8} + \frac{πn}{4}

y, sin (x + y) + sin (y + z) + sin (x + z) = 0

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

2 sin^{2} (x) - 13 sin (x) + 6 = 0

2 tan (θ) + 3 = 0

tan (x) = \frac{4}{6}