cos^2(θ)+2sin(θ)cos(θ)-sin^2(θ)=0

Solución

cos^{2} (θ) + 2 sin (θ) cos (θ) - sin^{2} (θ) = 0

θ = πn - \frac{π}{8}, θ = πn + \frac{π}{2} - \frac{π}{8}

Pasos de solución

cos^{2} (θ) + 2 sin (θ) cos (θ) - sin^{2} (θ) = 0

Re-escribir usando identidades trigonométricas

cos^{2} (θ) + sin (2 θ) - sin^{2} (θ) = 0

Re-escribir usando identidades trigonométricas

2 sin (2 θ + \frac{π}{4}) = 0

Dividir ambos lados entre

2

sin (2 θ + \frac{π}{4}) = 0

Soluciones generales para

sin (2 θ + \frac{π}{4}) = 0

2 θ + \frac{π}{4} = 0 + 2 πn, 2 θ + \frac{π}{4} = π + 2 πn

Resolver

2 θ + \frac{π}{4} = 0 + 2 πn : θ = πn - \frac{π}{8}

Resolver

2 θ + \frac{π}{4} = π + 2 πn : θ = πn + \frac{π}{2} - \frac{π}{8}

θ = πn - \frac{π}{8}, θ = πn + \frac{π}{2} - \frac{π}{8}

sin (x) - cos (x) = 0, 0 \leq x \leq 2 π

tan (x) + tan^{2} (x) = 0

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

sin (2 θ) + 2 sin (θ) = 0

tan (\frac{x}{2} + π) + 1 = 0