-sin(2x)=sin(4x)

Solución

- sin (2 x) = sin (4 x)

x = πn, x = \frac{π + 2 πn}{2}, x = \frac{π ( 3 n + 1 )}{3}, x = \frac{π ( 3 n + 2 )}{3}

Pasos de solución

- sin (2 x) = sin (4 x)

Restar

sin (4 x)

de ambos lados

- sin (2 x) - sin (4 x) = 0

Sea:

u = 2 x

- sin (u) - sin (2 u) = 0

Re-escribir usando identidades trigonométricas

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

Factorizar

- sin (u) - 2 cos (u) sin (u) : - sin (u) (2 cos (u) + 1)

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

Resolver cada parte por separado

sin (u) = 0 or 2 cos (u) + 1 = 0

sin (u) = 0 : u = 2 πn, u = π + 2 πn

2 cos (u) + 1 = 0 : u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn

Combinar toda las soluciones

u = 2 πn, u = π + 2 πn, u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn

Sustituir en la ecuación

u = 2 x

2 x = 2 πn : x = πn

2 x = π + 2 πn : x = \frac{π + 2 πn}{2}

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

2 x = \frac{4 π}{3} + 2 πn : x = \frac{π ( 3 n + 2 )}{3}

x = πn, x = \frac{π + 2 πn}{2}, x = \frac{π ( 3 n + 1 )}{3}, x = \frac{π ( 3 n + 2 )}{3}

sin (x) = - 0.61

2 cos (3 x) + 2 = 0

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

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

sin (θ) - 2 sin (θ) cos (θ) = 0