cos(θ)=-cos(2θ)

Solución

cos (θ) = - cos (2 θ)

θ = \frac{π}{3} + \frac{4 πn}{3}, θ = π + \frac{4 πn}{3}

Pasos de solución

cos (θ) = - cos (2 θ)

Restar

- cos (2 θ)

de ambos lados

cos (θ) + cos (2 θ) = 0

Re-escribir usando identidades trigonométricas

2 cos (\frac{3 θ}{2}) cos (\frac{θ}{2}) = 0

Resolver cada parte por separado

cos (\frac{3 θ}{2}) = 0 or cos (\frac{θ}{2}) = 0

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

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

Combinar toda las soluciones

θ = \frac{π}{3} + \frac{4 πn}{3}, θ = π + \frac{4 πn}{3}, θ = π + 4 πn, θ = 3 π + 4 πn

Mezclar intervalos sobrepuestos

θ = \frac{π}{3} + \frac{4 πn}{3}, θ = π + \frac{4 πn}{3}

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

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

θ, ma = t sin (θ) - m g

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

\frac{cot ( a )}{cos ( a )} = cos (a)