cos(5x)-sin(2x)-cos(x)=0

Solución

cos (5 x) - sin (2 x) - cos (x) = 0

x = πn, x = \frac{π}{2} + πn, x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Pasos de solución

cos (5 x) - sin (2 x) - cos (x) = 0

Re-escribir usando identidades trigonométricas

- sin (2 x) - 2 sin (2 x) sin (3 x) = 0

Factorizar

- sin (2 x) - 2 sin (2 x) sin (3 x) : - sin (2 x) (2 sin (3 x) + 1)

- sin (2 x) (2 sin (3 x) + 1) = 0

Resolver cada parte por separado

sin (2 x) = 0 or 2 sin (3 x) + 1 = 0

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

2 sin (3 x) + 1 = 0 : x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Combinar toda las soluciones

x = πn, x = \frac{π}{2} + πn, x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

cosh (4 x) = 0

x, tan (2 x) = - \frac{( \frac{30 + 20}{2} )}{80}

4 cos (3 θ) = 2

sin (x) = - 0.8176

sin (x) = - 0.342